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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 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 ...
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 ...
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 will talk about the inviscid limit of 2-D incompressible Navier-Stokes equations in the whole space with vortex sheet initial data. Although the initial data have different velocities ...
This talk concerns the instantaneous blowup of entropy-bounded classical solutions to the vacuum free boundary problem or the Cauchy problem of nonisentropic compressible Navier-Stokes equations.
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...
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...
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 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....
In this talk I will talk about our recent work on the three dimensional stochastic Navier-Stokes equations via convex integration method. First we establish non-uniqueness in law, existence and non-un...
Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on . We prove the enhanced dissipation phenomenon for the linearized isentropic compressible Navi...
The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left precondition...
This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme base...

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