相关论文: Global Behavior of Spherically Symmetric Navier-St…

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…

In this paper, the Cauchy problem for the one-dimensional (1-D) isentropic compressible Navier-Stokes equations (\textbf{CNS}) is considered. When the viscosity $\mu(\rho)$ depends on the density $\rho$ in a sublinear power law ($…

This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key…

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

This paper is devoted to the large time behavior of weak solutions to the three-dimensional Vlasov-Navier-Stokes system set on the half-space, with an external gravity force. This fluid-kinetic coupling arises in the modeling of…

We study free boundary compressible viscous models that may include nonlinear viscosities. These are compressible/incompressible Navier-Stokes type systems for a non-Newtonian stress tensor. They describe the motion of a possibly…

We prove existence and asymptotic stability of the stationary solution for the compressible Navier-Stokes equations for isentropic gas dynamics with a density dependent diffusion in a bounded interval. We present the necessary conditions to…

In this paper we establish the local-in-time existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in three-dimensional space. The vanishing density and temperature…

This paper proves the nonlinear asymptotic stability of the Lane-Emden solutions for spherically symmetric motions of viscous gaseous stars if the adiabatic constant $\gamma$ lies in the stability range $(4/3, 2)$. It is shown that for…

This paper concerns the stabilizing effect of viscosity on the vortex sheets. It is found that although a vortex sheet is not a time-asymptotic attractor for the compressible Navier-Stokes equations, a viscous wave that approximates the…

In this paper, we investigate the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient driven by multiplicative stochastic noise. We consider three-dimensional periodic domain and prove that the…

The two-phase free boundary value problem for the isothermal Navier-Stokes system is studied for general bounded geometries in absence of phase transitions, external forces and boundary contacts. It is shown that the problem is well-posed…

In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes…

This paper is devoted to the global existence of weak solutions to the three-dimensional compressible Navier-Stokes equations with heat-conducting effects in a bounded domain. The viscosity and the heat conductivity coefficients are assumed…

For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…

We consider the gravitational Navier-Stokes-Poisson equations with the equation of state $P(\rho)=K\rho^{\gamma}$, where $\gamma\in(\frac{6}{5},\frac{4}{3}]$, which models the viscous polytropic gaseous stars. We prove the existence of…

We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures.

Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…

This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…