arXiv subjects

Jiahong Wu

Publications and source records attributed to Jiahong Wu.

At least 19 recordsLinked to original sources

arXiv2026

Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields

We prove the global well-posedness and nonlinear stability of classical solutions to the three-dimensional compressible viscous, non-resistive MHD system on $\mathbb{T}^3$ near the equilibrium $(1,\mathbf{0},\mathbf{e}_3)$, for small $x_3$-symmetric perturbations and without any Diophantine condition on the background magnetic field. The central obstruction is the $x_3$-independent sector, in which the density and the magnetic field possess no dissipation, no damping, and no decay. We overcome it by exhibiting a hidden wave structure for the exact total pressure $\mathcal{D}=P(1+a)+B_3+\frac12|\mathbf{B}|^2$, the averaged pair $(\overline{\mathbf{u}},\overline{\mathcal{D}})$ obeys a closed system, and $\overline{\mathcal{D}}$ satisfies a strongly damped wave equation whose principal wave part propagates at the fast magnetosonic speed and whose non-parabolic branch damps at a rate that involves no gain of derivatives. This hidden damping substitutes for the missing magnetic dissipation, and simultaneously absorbs the magnetic pressure $\frac12\nabla|\mathbf{B}|^2$, the main obstruction created by compressibility. Together with a damped wave structure for the oscillatory sector and space-time weighted energy functionals with shifted time weights, this yields global existence, uniform stability, and explicit polynomial decay rates.

math.AP↗

arXiv2026

Linear Growth and Nonlinear Stability of Two-Dimensional MHD Couette Flow with Vertical Dissipation

We study the two-dimensional incompressible magnetohydrodynamic system near the Couette equilibrium $\bigl((y,0)^{\rm T},(β,0)^{\rm T}\bigr)$ on $\mathbb T\times\mathbb R$, in the anisotropic regime where both viscosity and magnetic diffusivity act only in the vertical direction. For the inviscid linearized problem with $|β|>1/2$, we prove sharp linear-in-time growth of the vorticity and current density at the level of the time rate. In contrast, the horizontal components of the velocity and magnetic perturbations remain uniformly bounded, while the vertical components exhibit quantitative inviscid damping at the rate $\langle t\rangle^{-1}$. For the nonlinear problem, we introduce shear-adapted Fourier multipliers that simultaneously capture enhanced dissipation, critical-time effects, and echo-type resonant interactions. Under a suitable horizontal background magnetic field and a quantitative compatibility condition between the magnetic field strength, viscosity, and magnetic diffusivity, we establish global nonlinear stability for divergence-free perturbations satisfying $ \left\| \bigl( \mathbf v_{\rm in}-(y,0)^{\rm T}, \mathbf H_{\rm in}-(β,0)^{\rm T} \bigr) \right\|_{H^N} \leq \varepsilon_0\min\{μ,ν\}^{1/2}, N\geq4$. Moreover, the nonzero horizontal Fourier modes decay in a shear-adapted $H^N$ norm at the enhanced-dissipation rate $e^{-c\min\{μ,ν\}^{1/3}\,t},$ and the vertical velocity and magnetic components gain an additional inviscid-damping factor $\langle t\rangle^{-1}$.

math.AP↗

arXiv2026

Time-asymptotic stability of generic Riemann solutions for the system of heat-conductive ideal gas without viscosity

This paper is concerned with the time-asymptotic stability of the generic Riemann solution for the one-dimensional system of heat-conductive ideal gas without viscosity, where the generic Riemann solution consists of a shock, a contact discontinuity, and a rarefaction wave. We prove that, as time tends to infinity, the solution of the non-viscous and heat-conductive ideal gas system converges uniformly to a composite wave composed of rarefaction wave, viscous contact wave, and viscous shock wave with a time-dependent shift. Motivated by the recent work of Kang-Vasseur-Wang [Arch. Ration. Mech. Anal. 249: 42 (2025)], we overcome the difficulties arising from the concurrence of shock and rarefaction waves for the partially dissipative hyperbolic-parabolic system with dissipation acting only on a single variable. More notably, the absence of velocity dissipation gives rise to new and intrinsic difficulties when handling the terms associated with the density and velocity. To resolve this, we exploit the precise structure of the governing equations and the additional properties of shock waves. Furthermore, we utilize the wave structure of the system without viscosity and perform separate space-time estimates for the density and velocity.

math.AP↗

arXiv2026

Stabilization by a background magnetic field: global well-posedness of the compressible isentropic ideal MHD equations with velocity damping

We study the Cauchy problem for the three-dimensional isentropic compressible ideal (inviscid and non-resistive) magnetohydrodynamic equations with velocity damping on the periodic torus $\mathbb{T}^3$. The system admits a steady equilibrium consisting of a constant density $\barρ$ and a uniform background magnetic field $ω\in\mathbb{R}^3$. We prove that this equilibrium is nonlinearly stable. More precisely, we show that if the initial data are a sufficiently small perturbation of $(\barρ,\mathbf{0},ω)$ in the Sobolev space $H^N(\mathbb{T}^3)$ with $N\geq 6r+4$, and if $ω$ satisfies a Diophantine condition, then the system admits a unique global smooth solution. Moreover, the perturbations decay algebraically in time. To the best of our knowledge, this is the first global well-posedness result for the multi-dimensional isentropic compressible ideal MHD system. The proof reveals a hidden dissipation mechanism: although neither the density equation nor the magnetic field equation contains explicit diffusion or damping, the coupling between the velocity and the magnetic field through the background field $ω$, combined with a Diophantine--Poincaré inequality, generates effective dissipation for both the density perturbation and the magnetic field perturbation, which together with the velocity damping yields global regularity and time decay.

math.AP↗

arXiv2026

Stabilization by a background magnetic field: global well-posedness of the full compressible viscous non-resistive MHD system without heat-conductivity

We consider the three-dimensional full compressible magnetohydrodynamic(MHD) system on the periodic torus $\mathbb T^3$ in the regime where the only dissipative mechanism acting on the system is the viscosity of the fluid: the magnetic field is non-resistive and the flow is non-heat-conducting. We prove that this system admits a unique global smooth solution, together with explicit algebraic decay rates, provided that the perturbation $(\mathbf u_0,\,P_0-\bar P,\,\mathbf H_0-\mathbf n)$ of the equilibrium state $(\mathbf 0,\bar P,\mathbf n)$ is sufficiently small in a high-order Sobolev space and the background magnetic field $\mathbf n\in\mathbb R^3$ satisfies a Diophantine condition. No smallness whatsoever is imposed on the initial density: it is only required to be bounded away from vacuum and from infinity, and may exhibit arbitrarily large variations. The proof uncovers a hidden dissipation mechanism. Although neither the density, nor the pressure, nor the magnetic field is endowed with any diffusion or damping of its own, the coupling of these quantities with the velocity through the background field $\mathbf n$, combined with a Poincaré-type inequality of Diophantine origin, generates effective dissipation for both the pressure and the magnetic field perturbations. The large variations of the density are handled by a two-tier energy argument, in which weighted time-decay estimates for the intermediate-order energy compensate exactly for the linear-in-time growth of the highest-order norm of the density.

math.AP↗

arXiv2026

DreamX-Creator: Democratizing Native Audio-Video Generation at 2K Resolution

Recent video generators often omit audio or synthesize it in a separate stage, limiting reciprocal modeling of visual dynamics and acoustic events. We present DreamX-Creator 1.0, a compact native joint audio-video generation system centered on a 7B generator. Conditioned on a first frame and a text prompt, the generator jointly denoises modality-specialized audio and video streams. The streams are processed independently in the first half of the network and coupled in the latter half through Gated Cross-Modal Attention, whose token- and head-wise output gates modulate each active cross-modal attention-head output. A unified Audio-Video Data System constructs and filters temporally coherent clips, produces structured multimodal annotations, and organizes clips into capability-oriented data pools. Progressive Joint Training comprises two audio-video pre-training stages followed by High-Quality Finetuning. Audio-Video Reinforcement Learning further post-trains the generator with Modality-Aware Multimodal Feedback that routes video-, audio-, and cross-modal feedback to the corresponding streams. For high-resolution output, our Autoregressive 1-Step 2K Refinement pipeline adapts a bidirectional multi-step teacher into an autoregressive multi-step refiner and distills it into a student requiring one denoising evaluation per temporal chunk. Overall, DreamX-Creator 1.0 achieves native, synchronized audio-video generation with performance competitive with state-of-the-art open-source systems. By releasing our compact 7B generator and 2K Refiner, we seek to democratize native audio-video generation and provide an accessible foundation for future research in unified audio-video generative modeling.

cs.CV↗

arXiv2026

FADE: From Passive Verification to Active Discovery in Counterfactual Video Understanding

Counterfactual video understanding evaluates whether models grasp physical and commonsense regularities. However, existing multiple-choice question (MCQ) benchmarks inadvertently leak target events through their questions and candidate options. This reduces the core challenge from active discovery to text-guided verification. In this paper, we present FADE, an effective training framework for counterfactual discovery and explanation. Our method is built on an evidence-first, two-stage training paradigm. First, evidence-internalized supervised fine-tuning grounds the model's predictions in decisive visual anomalies. Second, we apply a fading-anchor reinforcement learning strategy that progressively removes textual guidance, compelling the model to independently discover and explain evidence. To rigorously evaluate this capability, we also introduce an effective pipeline that converts existing MCQ datasets into aligned MCQ, open-ended question answering (OQA), and captioning tasks without requiring additional data curation. Our simple approach yields strong results. Using Qwen3-VL-8B as the baseline, FADE achieves state-of-the-art strict paired scores across all three tasks on DualityVidQA-test and IPV-Bench, outperforming GPT-5.6. In specific, when transitioning from constrained MCQs to unconstrained OQA and captioning, our model demonstrates remarkable robustness. Its performance retention is 90.4% and 67.4% on DualityVidQA-test-substantially higher than the 48.1% and 30.7% retained by GPT-5.6. We hope this simple framework can serve as a solid baseline for future research in unconstrained counterfactual video understanding.

cs.CV↗

arXiv2026

A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations

Huang and Shen developed a novel class of high-order BDF-IMEX consistent-splitting schemes for the incompressible Navier-Stokes equations, giving the first rigorous stability and error analysis for a fully decoupled splitting scheme of temporal order higher than two. Extending their analysis from unit viscosity to arbitrary viscosity, this work reveals that the error upper bound coefficient contains inverse powers of the viscosity. Our numerical experiments show that the scheme can break down at high Reynolds number. To save the scheme from this failure, we stabilize it by adding to the velocity update a symmetric positive-semidefinite spectral vanishing viscosity operator, built from the directionally applied Maday-Kaber-Tadmor kernel, which selectively damps the high, under-resolved modes at no additional asymptotic cost and leaves the structure of the error analysis intact. We establish stability and error estimates for the stabilized scheme in which the spectral vanishing viscosity provides viscosity-independent coercive control of the high modes. Three two-dimensional tests demonstrate the robustness and accuracy of the stabilized scheme. For a manufactured solution, the stabilized scheme retains its design order for k=2,3,4, whereas the unstabilized scheme diverges. For a perturbed Kovasznay flow, it accurately resolves the boundary layer at Re=10^4 and drives the perturbation back to the steady state, while the unstabilized scheme blows up. For the Kelvin-Helmholtz instability problem, it reproduces the reference integral diagnostics throughout the reliable regime, whereas the unstabilized scheme produces spurious solutions or blows up.

math.NA↗

arXiv2026

Global uniform regularity and large time behavior of solutions to three dimensional compressible MHD equations with vanishing vertical magnetic resistivity in half space

This paper aims to establish the global regularity and large time behavior of solutions to the three-dimensional (3D) compressible magnetohydrodynamics (MHD) equations with vanishing vertical magnetic resistivity in the upper half-space with no-slip boundary condition on velocity and perfectly conducting boundary condition on magnetic field. By exploiting anisotropic Sobolev inequalities and elaborated estimates, we are able to achieve global-in-time uniform regularity estimates of solutions, which are independent of small vertical resistivity coefficient $\varepsilon$. These uniform global regularity estimates allow us to pass to the limit as $\varepsilon \to 0$ and obtain the convergence to the corresponding MHD system without vertical magnetic resistivity globally in time. Moreover, the $H^{1}\left(\mathbb{R}_{+}^{3}\right)$ decay rates of solutions to the original system are also derived based on the detailed analysis on semigroup of the related linearized operator in half space and the uniform energy estimates achieved. In contrast to the decay estimates for the limit system obtained by Gao and Xie \cite{JDE}, the present decay estimate exhibits a slower rate, attributable to the absence of higher-order normal derivative estimates, which results from the occurrence of boundary layers. Finally, we combine both sets of regularity and decay results to rigorously prove an explicit time-uniform $L^2$ convergence rate of order $\varepsilon^{\frac{1}{4}}$ for the vanishing vertical magnetic resistivity limit process.

math.AP↗

arXiv2026

Learning Explicit Physical Parameter Control and Benchmarking for Video Generation

Recent advances in image-to-video generation have improved visual realism, making physically grounded and controllable dynamics an important step toward future world simulation. Current models often generate plausible motion, but it is not reliably governed by explicit physical causes, and instance-level constraints can leak or become entangled in multi-object interactions. We attribute this gap to two missing pieces: large-scale, fine-grained physical parameterization, and model designs that correctly bind physical attributes to instances and emphasize dynamics over appearance. To bridge this gap, we introduce PhyParam-Dataset, an interaction-centric collection of 130K physically simulated videos with dense physical parameterization, including force vectors, object material properties, and environmental constants across five representative rigid-body motion types. Built on this data, we present PhyParam, a physics-guided image-to-video diffusion model that conditions on object-level forces, masses, friction, restitution, and scene-level gravity via a lightweight physical-attention routing mechanism, and further improves motion learning with semantic-structural feature-space supervision. We also establish PhyParam-Bench, a benchmark for physical-law consistency in image-to-video generation, with a multi-level protocol evaluating temporal dynamics, spatial stability, and semantic--physical alignment. Experiments show that PhyParam improves physical consistency while maintaining high visual fidelity, advancing explicit rigid-body physical-parameter control for image-to-video generation. We will publicly release the dataset, benchmark, and code to support future research.

cs.CV↗

arXiv2026

Stability for the Boussinesq Equations with Horizontal Dissipation near the Hydrostatic Balance on $\mathbb{R}^2$

The hydrostatic balance is a fundamental equilibrium state in stratified fluids and plays a central role in geophysical fluid dynamics. Understanding its stability under incomplete dissipation is a longstanding challenge, since anisotropic diffusion alone is generally insufficient to control the nonlinear evolution and no robust stabilizing mechanism is known for the corresponding anisotropically dissipative Navier--Stokes equations. In this paper, we investigate the two-dimensional Boussinesq equations on $\mathbb{R}^2$ with only horizontal dissipation near the hydrostatic equilibrium $(U,Θ)=(0,x_2)$. We show that the velocity--temperature coupling generates internal gravity waves whose dispersive decay, together with the horizontal dissipation, provides an effective stabilizing mechanism that compensates for the complete absence of vertical dissipation. This identifies a mechanism by which dispersive wave propagation restores stability in an incompletely dissipative fluid system. For sufficiently small initial perturbations in $H^k(\mathbb{R}^2)\cap W^{3,1}(\mathbb{R}^2)$ with $k\ge14$, we establish the global existence and uniqueness of classical solutions together with explicit anisotropic, componentwise large-time decay rates for the velocity and temperature, including faster decay of the vertical velocity.

math.AP↗

arXiv2026

Nonlinear stability of a background magnetic field for the 3D compressible MHD equations with anisotropic dissipation

We study the nonlinear stability of an equilibrium with a background magnetic field for the three-dimensional compressible magnetohydrodynamic (MHD) equations in the whole space $\mathbb{R}^3$, in the strongly anisotropic regime where the velocity is dissipated only in the horizontal directions and the magnetic field is diffused in a single direction. We prove that for initial data sufficiently close to the equilibrium in a Sobolev space, the system admits a unique global-in-time solution that remains close to the equilibrium and enjoys quantitative dissipation estimates. The proof overcomes the severe lack of dissipation through two mechanisms: the background magnetic field is shown to generate enhanced dissipation for the magnetic field and the density, while a nonlinear cancellation mechanism is devised to resolve the loss of vertical derivatives caused by the compressible coupling.

math.AP↗

arXiv2026

Global stability and anisotropic large-time behavior of the three-dimensional compressible Navier--Stokes equations with eddy diffusion

We study the Cauchy problem for the three-dimensional compressible Navier--Stokes equations with eddy diffusion, an anisotropic dissipative mechanism that arises naturally in geophysical fluid dynamics (cf.~\cite{Jabin-Bresch-2018,Temam-Ziane-2004}). In contrast to the classical compressible Navier--Stokes system, the momentum equation here carries no full vertical Laplacian: the velocity is diffused only in the horizontal directions, and the sole vertical regularization it receives is the partial one transmitted through the compressible mode $\operatorname{div}\mathbf{u}$. This degeneracy invalidates the standard parabolic energy framework as well as the classical high--low frequency Green-function bounds. We prove that the constant non-vacuum equilibrium $(\barρ,0)$ is globally nonlinearly stable against small Sobolev perturbations: global classical solutions exist in $H^{N}(\mathbb{R}^{3})$ for every $N\ge 3$, and the density and velocity relax to equilibrium with explicit, genuinely anisotropic decay rates. The mechanism behind the result is a hidden dissipation produced by the pressure--divergence coupling between $\nablaρ$ and $\operatorname{div}\mathbf{u}$, which compensates for the missing vertical smoothing of the density and the compressible part of the velocity; the solenoidal part of the velocity, by contrast, is governed by a purely horizontal heat flow and therefore decays only at the two-dimensional rate. The analysis rests on a refined anisotropic spectral decomposition of the Green matrix, a div--curl treatment of the velocity, and time-weighted nonlinear energy estimates tailored to the degenerate dissipation. To the best of our knowledge, this is the first global stability and large-time behavior result for the three-dimensional compressible Navier--Stokes equations with eddy diffusion in the whole space.

math.AP↗

arXiv2026

Stability of vertically charged steady magnetic field in 3D incompressible magneto-micropolar fluids without magnetic and angular viscosity in a strip domain

This paper intends to understand the regularity and stability problem on the 3D incompressible magneto-micropolar equations with zero magnetic and angular viscosities in a strip domain. The magneto-micropolar system models the electrically conducting micropolar fluid in the presence of a magnetic field. The lack of magnetic diffusion and angular dissipation makes it impossible to prove even small data global well-posedness result, let alone general large data global regularity. This paper presents a steady-state setup around which any perturbations can be shown to be globally regular and stable. More precisely, any small perturbation near a steady magnetic field perpendicular to the horizontal boundary leads to a unique global classical solution. In addition, the solution is shown to converge to the steady state at an almost exponential rate as time goes to infinity. These appear to be the very first rigorous global results on the magneto-micropolar equations concerned here.

math.AP↗

arXiv2026

A consistent-splitting generalized scalar auxiliary variable scheme for the perturbed Boussinesq system

We propose and analyze a second-order consistent-splitting scheme, based on the generalized scalar auxiliary variable (GSAV) approach, for the two-dimensional perturbed Boussinesq system. The system is obtained by subtracting a stable, linearly stratified hydrostatic equilibrium from the standard Boussinesq system. The time discretization extends the consistent-splitting generalized BDF2 framework of Huang and Shen [17] for the Navier-Stokes equations, treating the nonlinear convection and advection together with the linear buoyancy and stratification couplings explicitly, so that each time step reduces to a small number of decoupled linear systems. We prove an unconditional weak stability theorem for the GSAV scheme and derive optimal second-order error estimates for the velocity, pressure, and temperature. A careful tracing reveals that the error constant depends on the inverse viscosity and inverse thermal diffusivity through a quadruply-nested exponential, so the scheme is not robust as either tends to zero. Numerical experiments confirm the second-order convergence and reproduce the expected internal-wave dynamics and exponential relaxation toward hydrostatic balance in a long-time stratified-flow simulation.

math.NA↗

arXiv2026

OmniDance: Multimodal Driven Dance Video Generation with Large-scale Internet Data

Music-driven dance video generation aims to synthesize expressive human motion that is temporally aligned with music while maintaining high visual fidelity. Despite recent progress, existing methods still face two key limitations: the lack of large-scale, high-quality dance video datasets, and the absence of principled frameworks for integrating music as a complementary conditioning signal into Video Generation Foundation Models. To address these limitations, we introduce CIPE-Dance, a large-scale Internet-sourced dance video dataset with choreography-informed text annotations, constructed via a progressive expert pipeline. To the best of our knowledge, CIPE-Dance is the largest dataset for dance video generation to date, comprising 300k high-quality clips over 400 hours and covering diverse dancers, environments, and dance genres. We further propose OmniDance, a framework-level recipe for integrating music into a TI2V foundation model without sacrificing its original controllability or visual fidelity. Motivated by the complementary roles of text as low-frequency semantics and music as high-frequency temporal dynamics, OmniDance co-designs a depth-aware specialization architecture, an anchored easy-to-hard curriculum learning strategy, and a modality-specialized time-dependent CFG strategy, enabling unified TI2V, MI2V, and MTI2V generation. Extensive experiments on CIPE-Dance demonstrate that OmniDance achieves state-of-the-art performance across all three tasks and exhibits robust multimodal integration capability. Project is available at https://github.com/AMAP-ML/OmniDance.

cs.CV↗

arXiv2026

Stabilizing effect of a background magnetic field on the 2D damped wave-type MHD equations

The stabilizing effect of a background magnetic field on electrically conducting fluids has been rigorously established for the standard MHD equations. This paper extends this theory to the more physically accurate damped wave-type MHD equations, where the induction equation is hyperbolic-parabolic and the velocity field has only vertical damping with no dissipation. These two features make the stability analysis harder than in the standard MHD setting. To overcome these difficulties, we design an energy functional exploiting the anisotropic structure, and discover a remarkable cancellation between the two most dangerous nonlinear terms by exploiting the full algebraic structure of the coupled system. As a consequence, we prove that any small perturbation near the background magnetic field is globally stable and establish optimal decay rates consistent with the 2D heat equation. To the best of our knowledge, this is the first rigorous stability result for the damped wave-type MHD equations near a background magnetic field.

math.AP↗

arXiv2026

Viscosity in error upper bound for a consistent splitting scheme of the Navier-Stokes equations

This paper investigates the role of viscosity in the error upper bounds of a consistent splitting scheme for the Navier-Stokes equations proposed by Huang and Shen [5]. In their original analysis the viscosity is fixed to unity. By following and extending their proof methodology while keeping the viscosity symbolic, we obtain an H1 velocity error bound that contains negative powers of viscosity, indicating that the scheme is not robust as viscosity tends zero. To establish this bound we refine a theorem in [8] on the constant in the Stokes pressure estimate, which is crucial to the error analysis. A targeted numerical experiment based on a perturbation of the Kovasznay flow corroborates this analytical prediction: the scheme of [5] blows up at high Reynolds number, and a comparison with a fully implicit Newton solver and with the time-dependent Stokes counterpart of the same scheme localizes the failure to the explicit treatment of the convection term.

math.NA↗