Huanyao Wen

Blow Up Criterion for Compressible Nematic Liquid Crystal Flows in Dimension Three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at a finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of the velocity gradient and the square of the maximum norm of the gradient of a liquid crystal director field.

Global Classical Large Solutions to Navier--Stokes Equations for Viscous Compressible and Heat-Conducting Fluids with Vacuum

In this paper, we consider the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids (i.e., the full Navier-Stokes equations). We get a unique global classical solution to the equations with large initial data and vacuum. Because of the strong nonlinearity and degeneration of the equations brought by the temperature equation and by vanishing of density (i.e., appearance of vacuum) respectively, to our best knowledge, there are only two results until now about global existence of solutions to the full Navier-Stokes equations with special pressure, viscosity and heat conductivity when vacuum appears (see \cite{Feireisl-book} where the viscosity

Global Spherically Symmetric Classical Solution to Compressible Navier–Stokes Equations with Large Initial Data and Vacuum

\mu=

GLOBAL SOLUTIONS OF A VISCOUS GAS-LIQUID MODEL WITH UNEQUAL FLUID VELOCITIES IN A CLOSED CONDUIT ∗

const and the so-called {\em variational} solutions were obtained, and see \cite{Bresch-Desjardins} where the viscosity

On global solutions to the viscous liquid–gas model with unconstrained transition to single-phase flow

\mu=\mu(\rho)

Global well-posedness and zero diffusion limit of classical solutions to 3D conservation laws arising in chemotaxis

degenerated when the density vanishes and the global weak solutions were got). It is open whether the global strong or classical solutions exist. By applying our ideas which were used in our former paper \cite{Ding-Wen-Zhu} to get

Global solutions to one-dimensional compressible Navier–Stokes–Poisson equations with density-dependent viscosity

H^3-

On the large time behavior of the compressible gas–liquid drift-flux model with slip

estimates of

A Stokes Two-Fluid Model for Cell Migration that Can Account for Physical Cues in the Microenvironment

u

Global classical solutions of viscous liquid–gas two-phase flow model

and