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高粘性渗出液严重阻碍伤口愈合,极易导致伤口恶化、感染以及持续炎症刺激,是临床伤口治疗的巨大挑战。理想的伤口敷料应该按需、及时地去除这些过量渗出液。然而,粘性生物流体的高粘度和弱流动性等固有特性强烈地阻碍了它的有效输运。在临床实践中,必须频繁采用外部物理方法,如生理盐水冲洗、物理擦除和负压治疗等方法去除粘性生物流体,不可避免的产生了继发性创伤和持续的疼痛刺激。因此,开发具有高效导出粘性生物流体能力的...
The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier–Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier...
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 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 ...
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 ...
This paper studies a Cauchy problem for a scalar multidimensional (multi-d) viscous convex conservation law, in which the initial data is a planar viscous shock with a multi-d periodic perturbation. W...
We prove the time-asymptotic stability of composite waves consisting of the superposition of a viscous shock and a rarefaction for the one-dimensional compressible barotropic Navier-Stokes equations. ...
We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting, solutio...
We are concerned with the three-dimensional incompressible Navier–Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}...
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...
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...
In this talk, I will discuss the method of convex integration and its applications on non-uniqueness of weak solutions to the hyper-viscous incompressible Navier-Stokes equations as well as the hypo-v...

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