Searcharxiv⌕ Search

arXiv subjects

Weike Wang

Publications and source records attributed to Weike Wang.

18 recordsLinked to original sources
arXiv2026

Wave propagation of a generic non--conservative compressible two--fluid model

The generalized Huygens principle for the Cauchy problem of a generic non-conservative compressible two-fluid model in R3 was established. This work fills a key gap in the theory, as previous results were confined to systems with full conservation laws or ``equivalent" conservative structures from specific compensatory cancellations in Green's function. Indeed, the genuinely non-conservative model studied here falls outside these categories and presents two major analytical challenges. First, its inherent non-conservative structure blocks the direct use of techniques (e.g., variable reformulation) effective for conservative systems. Second, its Green's function contains a -1-order Riesz operator associated with the fraction densities, which generates a so-called Riesz wave-IV exhibiting both slower temporal decay and poorer spatial integrability compared to the standard heat kernel, necessitating novel sharp convolution estimates with the Huygens wave. To overcome these difficulties, we develop a framework for precise nonlinear coupling, including interaction of Riesz wave-IV and Huygens wave. A pivotal step is extracting enhanced decay rates for the non-conservative pressure terms. By reformulating these terms into a product involving the fraction densities and the specific combination of fractional densities, and then proving this combination decays faster than the individual densities, we meet the minimal requirements for the crucial convolution estimates. This allows us to close the nonlinear ansatz by constructing essentially new nonlinear estimates. The success of our analysis stems from the model's special structure, particularly the equal-pressure condition. More broadly, the sharp nonlinear estimates developed herein is applicable to a wide range of non-conservative compressible fluid models.

math.AP↗
arXiv2026

Classical solutions to the Boltzmann equations for gas mixture with unequal molecular masses

The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while investigations into gas mixtures with unequal molecular masses remain relatively limited. Notably, mixed gas studies have broader applications exemplified by Earth's atmosphere, composed of 78\% nitrogen, 21\% oxygen, and 1\% trace gases, where the $N_2$ to $O_2$ molecular mass ratio is 28:32 (simplified as 7:8). This work addresses the Boltzmann equations for such mixtures with unequal molecular masses $(m^A\neq m^B)$, establishing the global in time existence of classical solutions near Maxwellians for soft potentials ($-3<\gamma<0$) in a periodic spatial domain. Our analysis encompasses arbitrary molecular mass ratios. Our analysis encompasses arbitrary molecular mass ratios. The main contribution of this paper lies in the detailed characterization of the linear collision operator's structure and establishing estimates for the nonlinear terms under unequal mass conditions. Consequently, these results may help advance spectral analysis for soft potentials as well as $L^2,L^{\infty}$ frameworks in future studies of multi-component Boltzmann equations.

math.AP↗
arXiv2025

Suppression of blow-up in 3-D Keller-Segel system with fractional diffusion via Couette flow in whole space

In this paper, we consider a Keller-Segel model with a fractional diffusion term in $\mathbb{R}^3$ in the background of a Couette flow. We show that when the background Couette flow is large enough, the dissipation enhancement induced could prevent the blow-up of solutions and thus prove the global existence and also obtain time decay rates of the solution in $L^p$ norm. The main tool of the proof is a corresponding Green's function and the key estimate is its $L^1$ estimate without singularities at $t=0$. To fulfill such an estimate, we meet great troubles caused by the fractional heat kernel together with the Couette flow in the model considered here and overcome the troubles by introducing a space-frequency mixed decomposition.

math.AP↗
arXiv2025

PHYBench: Holistic Evaluation of Physical Perception and Reasoning in Large Language Models

Current benchmarks for evaluating the reasoning capabilities of Large Language Models (LLMs) face significant limitations: task oversimplification, data contamination, and flawed evaluation items. These deficiencies necessitate more rigorous assessment methods. To address these limitations, we introduce PHYBench, a benchmark of 500 original physics problems ranging from high school to Physics Olympiad difficulty. PHYBench addresses data contamination through original content and employs a systematic curation pipeline to eliminate flawed items. Evaluations show that PHYBench activates more tokens and provides stronger differentiation between reasoning models compared to other baselines like AIME 2024, OlympiadBench and GPQA. Even the best-performing model, Gemini 2.5 Pro, achieves only 36.9% accuracy compared to human experts' 61.9%. To further enhance evaluation precision, we introduce the Expression Edit Distance (EED) Score for mathematical expression assessment, which improves sample efficiency by 204% over binary scoring. Moreover, PHYBench effectively elicits multi-step and multi-condition reasoning, providing a platform for examining models' reasoning robustness, preferences, and deficiencies. The benchmark results and dataset are publicly available at https://www.phybench.cn/.

cs.CL↗
arXiv2024

Enhanced dissipation and blow-up suppression for an aggregation equation with fractional diffusion and shear flow

In this paper, we consider an aggregation equation with fractional diffusion and large shear flow, which arise from modelling chemotaxis in bacteria. Without the advection, the solution of aggregation equation may blow up in finite time. First, we study the enhanced dissipation of shear flow by resolvent estimate method, where the fractional Laplacian $(-Δ)^{α/2}$ is considered and $α\in (0,2)$. Next, we show that the enhanced dissipation of shear flow can suppress blow-up of solution to aggregation equation with fractional diffusion and establish global classical solution in the case of $α\geq 3/2$. Here we develop some new technical to overcome the difficult of low regularity for fractional Laplacian.

math.AP↗
arXiv2024

Transition threshold for the 2-D Couette flow in whole space via Green's function

In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow $(y,0)$ at high Reynolds number $Re$ in whole space. By utilizing Green's function estimates for the linearized equations around Couette flow, we initially establish refined dissipation estimates for the linearized Navier-Stokes equations with a precise decay rate $(1+t)^{-1}.$ As an application, we prove that if the initial perturbation of vorticity satisfies$$\|ω_{0}\|_{H^{1}\cap L^1}\leq c_0ν^{\frac{3}{4}}$$ for some small constant $c_0$ independent of the viscosity $ν$, then we can reach the conclusion that the solution remains within $O\left( ν^{\frac{3}{4}}\right) $ of the Couette flow.

math.AP↗
arXiv2023

Suppression of blow-up in 3-D Keller-Segel model via Couette flow in whole space

In this paper, we study the 3-D parabolic-parabolic and parabolic-elliptic Keller-Segel models with Couette flow in $\mathbb{R}^3$. We prove that the blow-up phenomenon of solution can be suppressed by enhanced dissipation of large Couette flows. Here we develop Green's function method to describe the enhanced dissipation via a more precise space-time structure and obtain the global existence together with pointwise estimates of the solutions. The result of this paper shows that the enhanced dissipation exists for all frequencies in the case of whole space and it is reason that we obtain global existence for 3-D Keller-Segel models here. It is totally different from the case with the periodic spatial variable $x$ in [2,10]. This paper provides a new methodology to capture dissipation enhancement and also a surprising result which shows a totally new mechanism.

math.AP↗
arXiv2023

Enhanced dissipation and blow-up suppression for the three dimensional Keller-Segel equation with a non-shear incompressible flow

In this paper, we consider the Cauchy problem for the three dimensional parabolic-elliptic Keller-Segel equation with a large non-shear incompressible flow. Without advection, there exist solution with arbitrarily mass which blow up in finite time. Firstly, we introduce a three dimensional non-shear incompressible flow and study the enhanced dissipation of such flows by resolvent estimate method. Next, we show that the enhanced dissipation of such flow can suppress blow-up of solution to three dimensional parabolic-elliptic Keller-Segel equation and establish global classical solution with large initial data.

math.AP↗
arXiv2023

Pointwise space-time estimates of 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

Space-time behaviors for 3D compressible bipolar Navier-Stokes-Poisson system (BNSP) with unequal viscosities are given. The space-time estimate of electric field $\nablaϕ$ is the most important thing when deducing generalized Huygens' principle for BNSP since this estimate only can be obtained by $\nablaϕ=\frac{\nabla}Δ(ρ-n)$ from the Poisson equation. Thus, it requires to prove that the space-time estimate of $ρ-n$ only contains diffusion wave. The appearance of these unequal coefficients results that one cannot follow ideas for the special case, where the original system was rewritten as a compressible NS system and a compressible (unipolar) NSP system after a linear combination of unknowns. This linear combination brings special structure for nonlinear terms, and this structure was also used to get desired space-time estimate for $ρ-n$. Moreover, Green's function of the subsystem NSP does not contain Huygens wave is equally important in [36]. However, for the general case, the benefits from this linear combination will not exist any longer. First, we have to directly consider an $8\times8$ Green's matrix of the original system. Second, all of entries in Green's function in low frequency actually contain wave operators. This generally produces the Huygens' wave for each entry in Green's function, as a result, one cannot achieve that the space-time estimate of $ρ-n$ only contains the diffusion wave as usual. We overcome this difficulty by taking more detailed spectral analysis and developing new estimates arising from subtle cancellations in Green's function. Third, due to loss of the special structure of nonlinear terms from the linear combination, we shall develop new nonlinear convolution estimates such that we can ultimately obtain the expected space-time estimate for $\nablaϕ$ and further verify the generalized Huygens' principle.

math.AP↗
arXiv2021

Global well-posedness for a generalized Keller-Segel system with degenerate dissipation and mixing

We study the mixing effect for a generalized Keller-Segel system with degenerate dissipation and advection by a weakly mixing. Here the attractive operator has weak singularity, namely, the negative derivative appears in the nonlinear term by singular integral. Without advection, the solution of equation blows up in finite time. We show that the global well-posedness of solution with large advection. Since dissipation term degenerate into the damping, the enhanced dissipation effect of mixing no longer occurs, we prove that the mixing effect can weak the influence of nonlinear term. In this case, the mixing effect is similar with inviscid damping of shear flow. Combining to the mixing effect and damping effect of degenerate dissipation, the global $L^\infty$ estimate of solution is established.

math.AP↗
arXiv2021

In-situ tuned photoelectric properties of PtS$_2$ transistor

Strain engineering is a powerful and widely used strategy for boosting the performance of electronic and optoelectronic devices. Here, we demonstrate an approach to tune the photoelectric properties of Platinum sulfide (PtS$_2$) by using a ferroelectric substrate PMN-PT as the strain generator. It is found that both the drain current and responsivity of the PtS$_2$ photodetector is directly coupled to the electrostriction of PMN-PT, showing a high strain-tuned ratio $10^{3}$, high responsivity up to $6.3\times 10^{3}$ A/W and detectivity of $9.3\times 10^{12}$ Jones. Additionally, a high photogain $\approx 5\times 10^{5}$ is obtained at a gate voltage Vg = 15 V. Our results provide an effective method for manipulating electrical properties and optimizing performance of two dimensional layered (2D) materials based optoelectronic devices.

physics.app-ph↗
arXiv2021

Dissipation enhancement of planar helical flows and applications to three-dimensional Kuramoto-Sivashinsky and Keller-Segel equations

We introduce the planar helical flows on three dimensional torus and study the dissipation enhancement of such flows. We then use such flows as transport flows to solve the three dimensional advective Kuramoto-Sivashinsky and Keller-Segel equations. The global well-posedness of the Kuramoto-Sivashinsky equation is achieved when the linearized operator does not have growing mode in the direction orthogonal to the flow. The global classical solution of the three dimensional Keller-Segel is ensured for any size of the torus with arbitrarily large initial data.

math.AP↗
arXiv2019

Suppression of blow up by mixing in generalized Keller-Segel system with fractional dissipation

In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic Keller-Segel equation with fractional dissipation and the additional mixing effect of advection by an incompressible flow. Under suitable mixing condition on the advection, we study well-posedness of solution with large initial data. We establish the global $L^\infty$ estimate of the solution through nonlinear maximum principle, and obtain the global classical solution.

math.AP↗
arXiv2018

Decay of solutions to anisotropic conservation laws with large initial data

In this paper, we study the large time behavior of solutions to the Cauchy problem for the anisotropic conservation laws in two dimensional space. Without any smallness assumption on the initial data, the decay rates of solutions in $L^2$ space and homogeneous Sobolev space $\dot{H}^γ$ are obtained by using the method of time-frequency decomposition and the classical energy method.

math.AP↗
arXiv2016

Pointwise estimates for bipolar compressible Navier-Stokes-Poisson system in dimension three

The Cauchy problem of the bipolar Navier-Stokes-Poisson system (1.1) in dimension three is considered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit generalized Huygens' principle as the Navier-Stokes system. This phenomenon is the the most important difference from the unipolar Navier-Stokes-Poisson system. Due to non-conservative structure of the system (1.1) and interplay of two carriers which counteracts the influence of electric field (a nonlocal term), some new observations are essential for the proof. We make full use of the conservative structure of the system for the total density and total momentum, and the mechanism of the linearized unipolar Navier-Stokes-Poisson system together with the special form of the nonlinear terms in the system for the difference of densities and the difference of momentums. Lastly, as a byproduct, we extend the usual $L^2(\mathbb{R}^3)$-decay rate to $L^p(\mathbb{R}^3)$-decay rate with $p>1$ and also improve former decay rates in part.

math.AP↗
arXiv2016

Weak localization effect in topological insulator micro flakes grown on insulating ferrimagnet BaFe12O19

Many exotic physics anticipated in topological insulators require a gap to be opened for their topologica surface states by breaking time reversal symmetry. The gap opening has been achieved by doping magnetic impurities, which however inevitably create extra carriers and disorder that undermine the electronic transport. In contrast, the proximity to a ferromagnetic/ferrimagnetic insulator may improve the device quality, thus promises a better way to open the gap while minimizing the side-effects. Here, we grow thin single-crystal Sb1.9Bi0.1Te3 micro flakes on insulating ferrimagnet BaFe12O19 by using the van der Waals epitaxy technique. The micro flakes show a negative magnetoresistance in weak perpendicular fields below 50 K, which can be quenched by increasing temperature. The signature implies the weak localization effect as its origin, which is absent in intrinsic topological insulators, unless a surface state gap is opened. The surface state gap is estimated to be 10 meV by using the theory of the gap-induced weak localization effect. These results indicate that the magnetic proximity effect may open the gap for the topological surface attached to BaM insulating ferrimagnet. This heterostructure may pave the way for the realization of new physical effects as well as the potential applications of spintronics devices.

cond-mat.mes-hall↗
arXiv2012

Decay of the solution to the bipolar Euler-Poisson system with damping in $\mathbb{R}^3$

We construct the global solution to the Cauchy's problem of the bipolar Euler-Poisson equations with damping in $\mathbb{R}^3$ when $H^3$ norm of the initial data is small. If further, the $\dot{H}^{-s}$ norm ($0\leq s<3/2)$ or $\dot{B}_{2,\infty}^{-s}$ norm ($0<s\leq3/2$) of the initial data is bounded, we give the optimal decay rates of the solution. As a byproduct, the decay results of the $L^p-L^2$ ($1\leq p\leq2$) type hold without the smallness of the $L^p$ norm of the initial data. In particular, we deduce that $\|\nabla^k(ρ_1-ρ_2)\|_{L^2} \sim(1+t)^{-5/4-\frac{k}{2}}$ and $\|\nabla^k(ρ_i-\barρ,u_i,\nablaϕ)\|_{L^2} \sim(1+t)^{-3/4-\frac{k}{2}}$. We improve the decay results in Li and Yang \cite{Li3}(\emph{J.Differential Equations} 252(2012), 768-791), where they showed the decay rates as $\|\nabla^k(ρ_i-\barρ)\|_{L^2} \sim(1+t)^{-3/4-\frac{k}{2}}$ and $\|\nabla^k(u_i,\nablaϕ)\|_{L^2} \sim(1+t)^{-1/4-\frac{k}{2}}$, when the $H^3\cap L^1$ norm of the initial data is small. Our analysis is motivated by the technique developed recently in Guo and Wang \cite{Guo}(\emph{Comm. Partial Differential Equations} 37(2012), 2165-2208) with some modifications.

math.AP↗