arXiv subjects

Zhifei Zhang

Publications and source records attributed to Zhifei Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2026

Asymptotic stability threshold of the 2-D monotone shear flow with no-slip boundary condition

In this paper, we investigate the asymptotic stability threshold problem for the 2-D Navier-Stokes equations in a finite channel with no-slip boundary conditions, around monotone shear flow $(U(t,y),0)$. We establish that the flow is asymptotically stable under perturbations satisfying $\|u^{\mathrm{in}}\|_{H^2}\leq cν^{\frac12}$. To achieve the stability threshold $ν^{\frac{1}{2}}$, the key ingredients of the proof include: sharp resolvent estimates for the vorticity based on weak-type resolvent bounds; weighted space-time estimates for the vorticity; pointwise estimates for the velocity. Furthermore, we handle the nonlinear term through a divergence formulation, which facilitates the sharp application of the aforementioned space-time estimates.

math.AP↗

arXiv2026

On the classical solution for the steady triple-deck equations

This paper establishes the existence and uniqueness of classical solutions to the steady Triple-Deck equations, which describe incompressible boundary layer flow over localized roughness at high Reynolds numbers. The triple-deck theory was developed to overcome the Goldstein singularity in classical Prandtl boundary layer theory, capturing the interaction between the viscous sublayer, main layer, and upper layer when surface roughness of height $O({\rm Re}^{-\frac58})$ is present. The key ingredients of this paper include: (1) A decomposition separating roughness effects from nonlinear difficulties; (2) A novel Green's function using Airy functions that overcomes low-frequency singularities via the non-vanishing property of $\sqrt{3}Ai(z)+Bi(z)$; (3) The introduction of weighted Sobolev norms $\norm{|\p_x|^{\frac{1}{18}}y^{\frac16}ω}_{L^2}$ of the vorticity yielding $M$-independent estimates for displacement $A$. As a byproduct, local uniqueness of Couette flow is established when $F=0$.

math.AP↗

arXiv2025

OmniVCus: Feedforward Subject-driven Video Customization with Multimodal Control Conditions

Existing feedforward subject-driven video customization methods mainly study single-subject scenarios due to the difficulty of constructing multi-subject training data pairs. Another challenging problem that how to use the signals such as depth, mask, camera, and text prompts to control and edit the subject in the customized video is still less explored. In this paper, we first propose a data construction pipeline, VideoCus-Factory, to produce training data pairs for multi-subject customization from raw videos without labels and control signals such as depth-to-video and mask-to-video pairs. Based on our constructed data, we develop an Image-Video Transfer Mixed (IVTM) training with image editing data to enable instructive editing for the subject in the customized video. Then we propose a diffusion Transformer framework, OmniVCus, with two embedding mechanisms, Lottery Embedding (LE) and Temporally Aligned Embedding (TAE). LE enables inference with more subjects by using the training subjects to activate more frame embeddings. TAE encourages the generation process to extract guidance from temporally aligned control signals by assigning the same frame embeddings to the control and noise tokens. Experiments demonstrate that our method significantly surpasses state-of-the-art methods in both quantitative and qualitative evaluations. Video demos are at our project page: https://caiyuanhao1998.github.io/project/OmniVCus/. Our code, models, data are released at https://github.com/caiyuanhao1998/Open-OmniVCus

cs.CV↗

arXiv2025

Transition threshold for the Navier-Stokes-Coriolis system at high Reynolds numbers

The transition mechanism from laminar flow to turbulent flow is a central problem in hydrodynamic stability theory. To shed light on this transition mechanism, Trefethen et al.({\it \small Science 1993}) proposed the transition threshold problem, aiming to quantify the magnitude of perturbations required to trigger instability and determine their scaling with the Reynolds number. In this paper, we investigate the transition threshold of Couette flow for the three-dimensional incompressible Navier-Stokes-Coriolis system in the high Reynolds number regime ($\mathrm{Re}\gg 1$). By exploiting the combined effects of rotation (dispersion) and mixing mechanisms, we derive an improved stability threshold scaling in $\mathrm{Re}$. Precisely, we show that if the initial perturbation satisfies $$\|v_{in}-(y, 0, 0)\|_{\tilde{H}(\mathbb T \times \mathbb D)}\leq ε_0 \,\mathrm{Re}^{-α},$$ with any $α>\frac 23$ and $\tilde{H}=H^6 \cap W^{3,1}$ for $\mathbb D=\mathbb{R}^2$, and with any $α\geq\frac 56$ and $\tilde{H}=H^6$ for $\mathbb D=\mathbb{R}\times\mathbb{T}$, the corresponding solution of the Navier-Stokes-Coriolis system exists globally in time and remains asymptotically close to the Couette flow. The main analytical challenge arises from the anisotropic nature of the estimates for the zero modes and from the interactions between zero and non-zero modes, which we address using an anisotropic Sobolev space directly tailored to the zero modes. Additionally, we introduce a new dispersive structure for the zero modes and derive suitable Strichartz-type estimates. These tools enable us to exploit both the nonlinear structure and the improved dispersive behavior of certain good components of the zero modes, which play a crucial role in achieving the improved stability threshold.

math.AP↗

arXiv2025

Both Semantics and Reconstruction Matter: Making Representation Encoders Ready for Text-to-Image Generation and Editing

Modern Latent Diffusion Models (LDMs) typically operate in low-level Variational Autoencoder (VAE) latent spaces that are primarily optimized for pixel-level reconstruction. To unify vision generation and understanding, a burgeoning trend is to adopt high-dimensional features from representation encoders as generative latents. However, we empirically identify two fundamental obstacles in this paradigm: (1) the discriminative feature space lacks compact regularization, making diffusion models prone to off-manifold latents that lead to inaccurate object structures; and (2) the encoder's inherently weak pixel-level reconstruction hinders the generator from learning accurate fine-grained geometry and texture. In this paper, we propose a systematic framework to adapt understanding-oriented encoder features for generative tasks. We introduce a semantic-pixel reconstruction objective to regularize the latent space, enabling the compression of both semantic information and fine-grained details into a highly compact representation (96 channels with 16x16 spatial downsampling). This design ensures that the latent space remains semantically rich and achieves state-of-the-art image reconstruction, while remaining compact enough for accurate generation. Leveraging this representation, we design a unified Text-to-Image (T2I) and image editing model. Benchmarking against various feature spaces, we demonstrate that our approach achieves state-of-the-art reconstruction, faster convergence, and substantial performance gains in both T2I and editing tasks, validating that representation encoders can be effectively adapted into robust generative components.

cs.CV↗

arXiv2025

DiffusionBrowser: Interactive Diffusion Previews via Multi-Branch Decoders

Video diffusion models have revolutionized generative video synthesis, but they are imprecise, slow, and can be opaque during generation -- keeping users in the dark for a prolonged period. In this work, we propose DiffusionBrowser, a model-agnostic, lightweight decoder framework that allows users to interactively generate previews at any point (timestep or transformer block) during the denoising process. Our model can generate multi-modal preview representations that include RGB and scene intrinsics at more than 4$\times$ real-time speed (less than 1 second for a 4-second video) that convey consistent appearance and motion to the final video. With the trained decoder, we show that it is possible to interactively guide the generation at intermediate noise steps via stochasticity reinjection and modal steering, unlocking a new control capability. Moreover, we systematically probe the model using the learned decoders, revealing how scene, object, and other details are composed and assembled during the otherwise black-box denoising process.

cs.CV↗

arXiv2025

HBridge: H-Shape Bridging of Heterogeneous Experts for Unified Multimodal Understanding and Generation

Recent unified models integrate understanding experts (e.g., LLMs) with generative experts (e.g., diffusion models), achieving strong multimodal performance. However, recent advanced methods such as BAGEL and LMFusion follow the Mixture-of-Transformers (MoT) paradigm, adopting a symmetric design that mirrors one expert to another for convenient initialization and fusion, which remains suboptimal due to inherent modality discrepancies. In this work, we propose HBridge, an asymmetric H-shaped architecture that enables heterogeneous experts to optimally leverage pretrained priors from their respective modality domains. Unlike prior dense fusion strategies that straightforwardly connect all layers between experts via shared attention, HBridge selectively bridges intermediate layers, reducing over 40% attention sharing, which improves efficiency and enhances generation quality. Shallow and deep layers, which capture modality-specific representations, are decoupled, while mid-layer bridging promotes semantic alignment. To further strengthen cross-modal coherence, we introduce semantic reconstruction tokens that explicitly guide the generative expert to reconstruct visual semantic tokens of the target image. Extensive experiments across multiple benchmarks demonstrate the effectiveness and superior performance of HBridge, establishing a new paradigm for unified multimodal generation.

cs.CV↗

arXiv2025

The interaction between rough vortex patch and boundary layer

In this paper, we investigate the asymptotic behavior of solutions to the Navier-Stokes equations in the half-plane under high Reynolds number conditions, where the initial vorticity belongs to the Yudovich class and is supported away from the boundary. We establish the $L^p$ ($2\leq p< \infty$) convergence of solutions from the Navier-Stokes equations to those of the Euler equations. One of the main difficulties stems from the limited regularity of the initial data, which hinders the derivation of an asymptotic expansion. To overcome this challenge, we first prove a Kato-type criterion adapted to the Yudovich class setting. We then obtain uniform estimates for the Navier-Stokes equations -- a non-trivial task due to the strong boundary layer effects. A key component of our approach is the introduction of a suitable functional framework, which enables us to control the interaction between the rough vortex patch and the boundary layer.

math.AP↗

arXiv2025

Asymptotic stability of the symmetric flow via inviscid damping and enhanced dissipation

In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the non-slip boundary condition. As an immediate consequence, we prove the asymptotic stability of the symmetric flow in the high Reynolds number regime. Namely, if the initial velocity perturbation $u^{\mathrm{in}}$ satisfies $\Vert u^{\mathrm{in}}-(U(y),0) \Vert_{H^5}\leq c ν^{\frac{2}{3}}$, then inviscid damping and enhanced dissipation estimates also hold for the solution to the Navier-Stokes system.

math.AP↗

arXiv2025

Asymptotic stability of the Kolmogorov flow at high Reynolds numbers

In this paper we prove the asymptotic stability of the Kolmogorov flow on a non-square torus for perturbations $ω_0$ satisfying $\|ω_0\|_{H^3}\llν^{1/3}$, where $0<ν\ll1$ is the viscosity. Kolmogorov flows are important metastable states to the two dimensional incompressible Navier Stokes equations in the high Reynolds number regime. Our result shows that the perturbed solution will rapidly converge to a shear flow close to the Kolmogorov flow, before settling down to the Kolmogorov flow and slowly decaying to $0$ as $t\to\infty$. In fact, our analysis reveals several interesting time scales and rich dynamical behavior of the perturbation in the transition period $0<t\leq 1/ν$. The threshold $ν^{1/3}$, which is the same as that for the Couette flow, is quite surprising since one of the key stability mechanisms, enhanced dissipation, becomes considerably weaker in the case of Kolmogorov flows due to the presence of critical points. To overcome this essential new difficulty, we establish sharp vorticity depletion estimates near the critical points to obtain improved decay rates for the vorticity and velocity fields that are comparable with those for Couette flows, at least for our purposes. We then combine these estimates (enhanced dissipation, inviscid damping and vorticity depletion) with a quasilinear approximation scheme and a multiple-timescale analysis naturally adapted to the dynamics of the perturbation, to obtain the $ν^{1/3}$ threshold for dynamic stability of Kolmogorov flows. The threshold is expected to be sharp when the perturbation is considered in Sobolev spaces. This appears to be the first result that applies vorticity depletion estimates to improve thresholds for nonlinear asymptotic stability in incompressible fluid equations.

math.AP↗

arXiv2025

Baking Gaussian Splatting into Diffusion Denoiser for Fast and Scalable Single-stage Image-to-3D Generation and Reconstruction

Existing feedforward image-to-3D methods mainly rely on 2D multi-view diffusion models that cannot guarantee 3D consistency. These methods easily collapse when changing the prompt view direction and mainly handle object-centric cases. In this paper, we propose a novel single-stage 3D diffusion model, DiffusionGS, for object generation and scene reconstruction from a single view. DiffusionGS directly outputs 3D Gaussian point clouds at each timestep to enforce view consistency and allow the model to generate robustly given prompt views of any directions, beyond object-centric inputs. Plus, to improve the capability and generality of DiffusionGS, we scale up 3D training data by developing a scene-object mixed training strategy. Experiments show that DiffusionGS yields improvements of 2.20 dB/23.25 and 1.34 dB/19.16 in PSNR/FID for objects and scenes than the state-of-the-art methods, without depth estimator. Plus, our method enjoys over 5$\times$ faster speed ($\sim$6s on an A100 GPU). Our Project page at https://caiyuanhao1998.github.io/project/DiffusionGS/ shows the video and interactive results. The code and models are publicly available at https://github.com/caiyuanhao1998/Open-DiffusionGS

cs.CV↗

arXiv2025

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping

In this paper, we prove the Anderson localization near the spectral edge for some alloy-type Anderson-Bernoulli model on $\mathbb{Z}^d$ with exponential long-range hopping. This extends the work of Bourgain [Geometric Aspects of Functional Analysis, LNM 1850: 77--99, 2004], in which he pioneered a novel multi-scale analysis to treat Bernoulli random variables. Our proof is mainly based on Bourgain's method. However, to establish the initial scales Green's function estimates, we adapt the approach of Klopp [Comm. Math. Phys, Vol. 232, 125--155, 2002], which is based on the Floquet-Bloch theory and a certain quantitative uncertainty principle. Our proof also applies to an analogues model on $\mathbb{R}^d.$

math-ph↗

arXiv2025

The Second Order 2D Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime

We consider a system of $N$ bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normalized thickness of the box $d\ll1$. We assume particles to interact through a repulsive, radially symmetric and short-range interaction potential with scattering length scale $a\ll d$. We present a comprehensive study of such system in the Gross-Pitaevskii regime, up to the second order ground state energy, starting from proving optimal Bose-Einstein condensation results which were not previously available. The fine interplay between the parameters $N$, $a$ and $d$ generates three regions. Our result in one region on the one hand, is compatible with the classical three-dimensional Lee-Huang-Yang formula. On the other hand, it reveals a new mechanism exhibiting how the second order correction compensates and modifies the first order energy, which was previously thought of as containing a jump, and thus explains how a three-dimensional Bose gas system smoothly transits into two-dimensional system. Moreover, delving into the analysis of this new mechanism exclusive to the second order, we discover a dimensional coupling correlation effect, deeply buried away from the expected 3D and quasi-2D renormalizations, and calculate a new second order correction to the ground state energy.

math-ph↗

arXiv2025

Incompressible Euler limit from the Boltzmann equation with Maxwell reflection boundary condition in the half-space

In this paper, we rigorously justify the incompressible Euler limit of the Boltzmann equation with general Maxwell reflection boundary condition in the half-space. The accommodation coefficient $α\in (0,1]$ is assumed to be $O(1)$. Our construction of solutions includes the interior fluid part and Knudsen-Prandtl coupled boundary layers. The corresponding solutions to the nonlinear Euler and nonlinear Prandtl systems are taken to be shear flows. Due to the presence of the nonlinear Prandtl layer, the remainder equation loses one order normal derivative. The key technical novelty lies in employing the full conservation laws to convert this loss of the normal derivative into the loss of tangential spatial derivative, avoiding any loss of regularity in time. By working within an analytic $L^2 \mbox{-} L^\infty$ framework, we establish the uniform estimate on the remainder equations, thus justify the validity of the incompressible Euler limit from the Boltzmann equation for the shear flow case.

math.AP↗

arXiv2025

The second order Huang-Yang approximation to the Fermi thermodynamic pressure

We consider a dilute Fermi gas in the thermodynamic limit with interaction potential scattering length $\mathfrak{a}_0$ at temperature $T>0$. We prove the 2nd order Huang-Yang approximation for the Fermi pressure of the system, in which there is a 2nd order term carrying the positive temperature efffect.Our formula is valid up to the temperature $T<ρ^{\frac{2}{3}+\frac{1}{6}}$, which is, by scaling, also necessary for the Huang-Yang formula to hold. Here, $T_F\simρ^{\frac{2}{3}}$ is the Fermi temperature. We also establish during the course of the proof, a conjecture regarding the second order approximation of density $ρ$ by R. Seiringer \cite{FermithermoTpositive}. Our proof uses frequency localization techniques from the analysis of nonlinear PDEs and does not involve spatial localization or Bosonization. In particular, our method covers the classical Huang-Yang formula at zero temperature.

math-ph↗

arXiv2025

TRAIL: Transferable Robust Adversarial Images via Latent diffusion

Adversarial attacks exploiting unrestricted natural perturbations present severe security risks to deep learning systems, yet their transferability across models remains limited due to distribution mismatches between generated adversarial features and real-world data. While recent works utilize pre-trained diffusion models as adversarial priors, they still encounter challenges due to the distribution shift between the distribution of ideal adversarial samples and the natural image distribution learned by the diffusion model. To address the challenge, we propose Transferable Robust Adversarial Images via Latent Diffusion (TRAIL), a test-time adaptation framework that enables the model to generate images from a distribution of images with adversarial features and closely resembles the target images. To mitigate the distribution shift, during attacks, TRAIL updates the diffusion U-Net's weights by combining adversarial objectives (to mislead victim models) and perceptual constraints (to preserve image realism). The adapted model then generates adversarial samples through iterative noise injection and denoising guided by these objectives. Experiments demonstrate that TRAIL significantly outperforms state-of-the-art methods in cross-model attack transferability, validating that distribution-aligned adversarial feature synthesis is critical for practical black-box attacks.

cs.CV↗

arXiv2025

Extended states for the Random Schrödinger operator on $\mathbb{Z}^d$ ($d\geq 5$) with decaying Bernoulli potential

In this paper, we investigate the delocalization property of the discrete Schrödinger operator $H_ω=-Δ+v_nω_nδ_{n,n'}$, where $v_n=κ|n|^{-α}$ and $ω=\{ω_n\}_{n\in\mathbb{Z}^d}\in \{\pm 1\}^{\mathbb{Z}^d}$ is a sequence of i.i.d. Bernoulli random variables. Under the assumptions of $d\geq 5$, $α>\frac14$ and $0<κ\ll1$, we construct the extended states for a deterministic renormalization of $H_ω$ for most $ω$. This extends the work of Bourgain [{\it Geometric Aspects of Functional Analysis}, LNM 1807: 70--98, 2003], where the case $α>\frac13$ was handled. Our proof is based on Green's function estimates via a $6$th-order renormalization scheme. Among the main new ingredients are the proof of a generalized Khintchine inequality via Bonami's lemma, and the application of the fractional Gagliardo-Nirenberg inequality to control a new type of non-random operators arising from the $6$th-order renormalization.

math-ph↗

arXiv2025

Self-similar algebraic spiral vortex sheets of 2-D incompressible Euler equations

This paper provides the first rigorous construction of the self-similar algebraic spiral vortex sheet solutions to the 2-D incompressible Euler equations. These solutions are believed to represent the typical roll-up pattern of vortex sheets after the formation of curvature singularities. The most challenging part of this paper is to handle the Cauchy integral for the algebraic spiral curve, which falls outside the classical theory of singular integral operators.

math.AP↗