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Changsheng Dou

Publications and source records attributed to Changsheng Dou.

6 recordsLinked to original sources
arXiv2021

A New Upper Bound for the Largest Growth Rate of Linear Rayleigh--Taylor Instability

We investigate the effect of surface tension on the linear Rayleigh--Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with largest growth rate $Λ$ is proved under the instability condition (i.e., the surface tension coefficient $\vartheta$ is less than a threshold $\vartheta_{\rm c}$) by modified variational method of PDEs. Moreover we find a new upper bound for $Λ$. In particular, we observe from the upper bound that $Λ$ decreasingly converges to zero, as $\vartheta$ goes from zero to the threshold $\vartheta_{\rm c}$. The convergence behavior of $Λ$ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.

math-ph↗
arXiv2017

Global weak solutions to 3D compressible Primitive equations with density-dependent viscosity

This paper is devoted to investigating the global existence of weak solutions for the compressible primitive equations (CPE) with damping term in a three-dimensional torus for large initial data. The system takes into account density-dependent viscosity. In our proof, we represent the vertical velocity as a function of the density and the horizontal velocity which will play a role to use the Faedo-Galerkin method to obtain the global existence of the approximate solutions. Motivated by Vasseur and Yu [yucheng2016], we obtain the key estimates of lower bound of the density, the Bresch-Desjardin entropy on the approximate solutions. Based on these estimates, using compactness arguments, we prove the global existence of weak solutions of CPE by vanishing the parameters in our approximate system step by step.

math.AP↗
arXiv2014

Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces

We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier-Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain $R^d (d = 2, 3)$, provided that the Mach number is appropriately small. At the same time, the low Mach number limit is rigorously verified. The basic idea in the proof is to split the equations into two parts, one of which is similar to the steady incompressible Navier-Stokes equations with large forces, while another part corresponds to the steady compressible heat-conductive Navier-Stokes equations with small forces. The existence is then established by dealing with these two parts separately, establishing uniform in the Mach number a priori estimates and exploiting the known results on the steady incompressible Navier-Stokes equations.

math.AP↗
arXiv2012

Weak-strong uniqueness property for the compressible flow of liquid crystals

Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular direction with inhomogeneous Dirichlet boundary condition, new techniques are introduced to build up the relative entropy inequalities.

math.AP↗
arXiv2012

On One-dimensional Compressible Navier-Stokes Equations with Degenerate Viscosity and Constant State at Far fields

In this paper, we are concerned with the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity $μ(ρ)=ρ^α(α>0)$ and pressure $P(ρ)=ρ^γ\ (γ>1)$. We will establish the global existence and asymptotic behavior of weak solutions for any $α>0$ and $γ>1$ under the assumption that the density function keeps a constant state at far fields. This enlarges the ranges of $α$ and $γ$ and improves the previous results presented by Jiu and Xin. As a result, in the case that $0<α<\frac12$, we obtain the large time behavior of the strong solution obtained by Mellet and Vasseur when the solution has a lower bound (no vacuum).

math.AP↗