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We study the well/ill-posedness of the Boltzmann equation with dispersive methods. We take the constant collision kernel case as the 1st example. We construct a family of special solutions, which are ...
In this talk, time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We will di...
Boltzmann 方程是统计力学中的基本方程,被用来描述稀疏气体的运动,其解的整体适定性和大时间渐近行为是偏微分方程领域的重要问题。另一方面,Hilbert 于1912 年提出了Boltzmann 方程的Hilbert 展开,从形式上说明了Boltzmann 方程的一阶近似是可压缩Euler 方程。此后,从数学上严格证明Boltzmann 方程到可压Euler 方程的流体动力学极限一直是很多数学...
针对不可压缩理想磁流体方程自由边界问题的适定性,对有界初始区域的情形做较详细的阐述,并对相关的背景、研究进展和存在的问题作简要的介绍。
In recent years, the study of kinetic equations has attracted much attention because it involves many important scientific phenomena and fields of science, such as nuclear reactor diffusion phenomena,...
In this talk, we shall prove the global existence and the large time decay estimate of solutions to compressible Prandtl system with small initial data, which is analytical in the tangential variable....
In this talk, we consider the large time behavior of the weak solution to the free boundary problem for one-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosity and va...
We derive the classical compressible Euler equation as the limit of 3D quantum N-particle dynamics as N tends to infinity and Planck's constant tends to zero. We establish strong and quantitative conv...
2023年1月7-8日,由中国力学学会主办、大连理工大学承办的“中国力学学会第三届全国力学博士生学术论坛”以线上报告及交流的形式成功召开。大连理工大学力学系主任郭旭教授担任本次论坛主席。此次论坛得到了中国力学学会青年工作委员会与工业装备结构分析优化与CAE软件全国重点实验室的大力支持,并通过多个网络平台同步直播。
We study the global well-posedness problem for the 1d compressible Navier-Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (Commun Pure Appl Math 75(2):223-348, 2022) e...
We study the global well-posedness problem for the 1d compressible Navier-Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (Commun Pure Appl Math 75(2):223-348, 2022) e...
Hydrodynamic stability at high Reynolds number is a central topic in fluid mechanics. It is closely related to turbulence. Whereas the laminar velocity profile is linearly stable for all Reynolds numb...
We provide an unconditional $L^2$ upper bound for the boundary layer separation of 3D Leray--Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulen...
We develop a class of mixed finite element methods for the ferrofluid flow model proposed by Shliomis [Soviet Physics JETP, 1972]. We show that the energy stability of the weak solutions to the model ...
In this talk, we will discuss the resolvent problem for the linearized one of the free surface problem of compressible, viscous and heat-conducting fluid, which is a problem in an infinite strip domai...

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