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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global large strong solutions to the 2D radially symmetric compressible Navier-Stokes equations on bounded domain
有界域 二维径向对称 可压缩Navier-Stokes方程 全局大强解
2023/12/11
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Well-balanced positivity-preserving high-order discontinuous Galerkin methods for Euler equations with gravitation
引力 欧拉方程 高阶间断 Galerkin方法
2023/11/29
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Compressible fluid limit for the Landau equation
Landau方程 可压缩 流体极限
2023/11/29
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Geometric regularity criteria and inviscid limit of incompressible Navier--Stokes Equations under Navier boundary condition
Navier边界条件 不可压缩 Navier-Stokes方程 几何正则性准则 无粘极限
2023/11/29
We report our recent works on the analysis of 3D incompressible Navier--Stokes Equations subject to the Navier slip boundary condition, i.e., tangential components of the stress exerted by the normal ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： On the construction of solutions to some inviscid free boundary problems
无粘 自由边界 问题解 构造
2023/12/11
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the construction of solutions to some inviscid free boundary problems
无粘 自由边界 解构造
2023/11/15
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Blowup of smooth solutions for compressible Navier-Stokes equations
可压缩 Navier-Stokes方程 光滑解 爆破
2023/11/15
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 ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Linear reciprocal transformations of bihamiltonian integrable hierarchies
双哈密尔顿 可积层次 线性互易变换 流体力学
2023/11/13
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Cartan-Helgason theorem for quaternionic symmetric pairs
四元数 对称对 Cartan-Helgason定理
2023/11/7
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prandtl Boundary Layer in An Infinitely Long Convergent Channel
无穷长 收敛通道 Prandtl边界层
2023/11/7
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Finite-Time Splash for the free boundary incompressible Navier–Stokes equations (I)
自由边界 不可压缩 Navier-Stokes方程 有限时间飞溅
2023/5/18
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Isometric embedding and fluid mechanics
等距嵌入 流体力学 理论流体力学
2023/5/10
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：高维可压缩Navier-Stokes方程三类平面波形在空间周期扰动下的渐近稳定性
高维可压缩 Navier-Stokes方程 三类平面波形 空间周期扰动 渐近稳定性
2023/5/6
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Hyperbolic minimizing closed orbit and Herman's conjecture
双曲 最小化 闭合轨道 赫尔曼猜想
2023/5/6
We are motivated to study this problem so that the proof of Arnold Diffusion of many degrees of freedom can be significantly simplified.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time behavior of Alfven waves in a flowing plasma
阿尔文波 流动 等离子体 长期行为
2023/4/28
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 ...