Related papers: Vanishing viscosity of one-dimensional isentropic …
In this paper, we study the vanishing viscosity limit of one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity, to the isentropic compressible Euler equations. Based on several new uniform…
We prove the convergence of the vanishing viscosity limit of the one-dimensional, isentropic, compressible Navier-Stokes equations to the isentropic Euler equations in the case of a general pressure law. Our strategy relies on the…
We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the…
We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…
The vanishing viscosity limit of the two-dimensional (2D) compressible isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that…
We consider the compressible Navier-Stokes equation with density dependent viscosity coefficients, focusing on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions both in the torus and in the whole…
We prove the existence of relative finite-energy vanishing viscosity solutions of the one-dimensional, isentropic Euler equations under the assumption of an asymptotically isothermal pressure law, that is, $p(\rho)/\rho = O(1)$ in the limit…
We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $\Omega$. We show the convergence of the weak solution to the…
It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected with vacuum. Given a rarefaction wave with…
In this paper we study the vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. We show that, under suitable assumptions…
In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added…
In this paper we consider the barotropic compressible quantum Navier-Stokes equations with a linear density dependent viscosity and its limit when the scaled Planck constant vanish. Following recent works on degenerate compressible…
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for barotropic compressible fluids in $\mathbb{R}^3$. When the viscosity coefficients obey a lower power-law of the density (i.e., $\rho^\delta$…
This paper is concerned with the vanishing dissipation limiting problem of one-dimensional non-isentropic Navier-Stokes equations with shock data. The limiting problem was solved in 1989 by Hoff-Liu in [13] for isentropic gas with single…
We identify a class of measure-valued solutions of the barotropic Euler system on a general (un-bounded) spatial domain as a vanishing viscosity limit for the compressible Navier-Stokes system. Then we establish the weak…
In this paper we study a vanishing pressure process for highly compressible Navier-Stokes equations as the Mach number tends to infinity. We first prove the global existence of weak solutions for the pressureless system in the framework…
We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the vanishing viscosity limit, we show a…
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic stability of the viscous shock wave is established under some smallness conditions. The proof is given by an elementary…
In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order…
We obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity…