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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...
The scattering problems for elastic waves have recently received ever increasing attentions in both the engineering and mathematical communities for their important applications in geophysics and seis...
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...
In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equatio...
In this talk, we will discuss some recent progress on steady Navier-Stokes system in a channel, in particular, the problem posed by Leray on steady flows in channels. The existence and uniqueness of s...
A dispersive decay estimate is proven for the linear propagator of the three-scale rotating stratified Boussinesq equations in the stratification-dominant regime. Because the phase function of that pr...
A dispersive decay estimate is proven for the linear propagator of the three-scale rotating stratified Boussinesq equations in the stratification-dominant regime. Because the phase function of that pr...
复杂制造系统在生产过程中存在诸多的内外部风险。作为一个对初始条件极为敏感的混沌系统,即便是微小的风险,随着生产制造过程的推进,这些风险也会不断被传递、累计、放大,最终将极大拖延生产进度,或者是系统制造生产稳定性下降,严重时甚至造成整个复杂制造系统生产的混乱和中断。通过针对典型的复杂制造系统仿真数据,引入神经网络学习机制,建模系统风险因子与模型;基于熵理论和临界慢化理论完成复杂制造系统临界态物理指标...
Motivated by applications, like modeling of thin structures immersed in a fluid, we develop a well posedness theory for Newtonian and some non-Newtonian fluids under singular forcing in Lipschitz doma...
A brief introduction to Peridynamics model and a fast algorithm for the nonlocal unsteady problems is given in this talk. The POD algorithm can be employed in the numerical simulation of nonlocal diff...
In this talk, we will review the past developments on the solutions of the compressible Navier-Stokes equations and reveal the three hidden structures which linked the weak solution to the strong one....
可压缩Navier-Stokes方程描述可压缩粘性流体运动的力学规律,是流体力学中的基本方程。如果忽略粘性效应,可压缩Navier-Stokes方程即为无粘的可压缩Euler方程。可压缩Euler方程描述理想流体的运动,是典型的双曲守恒律方程组,其主要特点是:无论初值多么光滑和多么小,解都可能会爆破,形成间断(激波)。如果考虑可压缩Euler方程的Riemann问题,其解具有三种基本波:激波、稀疏...

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