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In this talk, I will present our recent result the 2D radially symmetric compressible Navier-Stokes equations with density-dependent viscosity. Under the condition of beta>1, we prove the global exist...
We develop high order discontinuous Galerkin (DG) methods with Lax-Friedrich fluxes for Euler equations under gravitational fields. Such problems may yield steady-state solutions and the density and p...
We are concerned with the compressible Euler limit for smooth solutions to the Landau equation with Coulomb potentials in the whole space. Specifically, over any finite time interval where the full co...
We will present our recent results on the local well-posedness of free boundary problems for some inviscid fluids. In particular, for each problem the solution is constructed as the vanishing viscosit...
We will present our recent results on the local well-posedness of free boundary problems for some inviscid fluids. In particular, for each problem the solution is constructed as the vanishing viscosit...
In this talk,we discuss the finite time blow up phenomena of smooth solutions to the compressible Navier-Stokes system when the initial data contain vacuums. It is proved that any classical solutions ...
For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transfo...
we present a joint work with Clemens Weiske and Genkai Zhang (Sweden). It shows a branching law for compact symmetric pairs K\subset G of quaternionic type. Precisely to say, K is a product of a simpl...
This talk is about the large Reynold number limits and asymptotic behaviors of solutions to the 2D steady Navier-Stokes equations in an infinitely long convergent channel. We will show that for a gene...
In this talk, we consider the incompressible Navier-Stokes equations with free boundary, which has a finite-time splash singularity for a large class of specially prepared initial data. The approach i...
In this talk, I first discuss isometric embedding from differential geometry and its relation with fluid mechanic equations. Then I will present recent progress and my works on isometric embeddings of...
疏散波(rarefaction wave)、激波(shock wave)和涡片波(vortex sheet)是可压缩流体中的三类基本波形,它们分别对应可压缩流体的疏散、压缩和剪切三类不同的物理现象。本次报告将研究对于可压缩Navier-Stokes方程,即考虑流体的粘性效应时,这三类波现象在小扰动下的稳定性。特别地,这里的扰动在空间无穷远处可以周期振荡,这类非局部扰动不仅带来数学上的新困难,也让我...
We are motivated to study this problem so that the proof of Arnold Diffusion of many degrees of freedom can be significantly simplified.
In this talk, we consider the long-time behavior of the linearized MHD equations around a steady flowing plasma. We confirm the following physical phenomenon: there will be a generation of a magnetic ...
由于油气资源的成分复杂,油藏工程师在描述原油的性质时,常常需要使用不同的数学模型。除了经典的黑油模型之外,还有诸如热采模型、裂缝模型、多重介质模型等。一些提高采收率技术通常基于更一般的组分模型框架来进行数值模拟,例如聚合物驱油剂、表面活化剂驱油剂、碱驱油剂、微生物驱油剂、低盐度水驱等。此外,二氧化碳埋藏、地下水污染治理、地热资源开采等应用问题也可使用组分模型来模拟。这些重要的应用使得多相多组分模拟...

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