On the inviscid limit for the compressible Navier-Stokes system in an impermeable bounded domain

Abstract

In this paper we investigate the issue of the inviscid limit for the compressible Navier-Stokes system in an impermeable fixed bounded domain. We consider two kinds of boundary conditions. The first one is the no-slip condition. In this case we extend the famous conditional result obtained by Kato in the homogeneous incompressible case. Kato proved that if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes then the solutions of the incompressible Navier-Stokes equations converge to some solutions of the incompressible Euler equations in the energy space. We provide here a natural extension of this result to the compressible case. The other case is the Navier condition which encodes that the fluid slips with some friction on the boundary. In this case we show that the convergence to the Euler equations holds true in the energy space, as least when the friction is not too large. In both cases we use in a crucial way some relative energy estimates proved recently by Feireisl, Ja Jin and Novotn{ý}.

References in corpus (4)

• Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
• Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
• Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition
• Incompressible flow around a small obstacle and the vanishing viscosity limit

Cited by in corpus (4)

• On the Euler+Prandtl expansion for the Navier-Stokes equations
• Vanishing viscosity limit for the compressible Navier-Stokes system via measure-valued solutions
• Euler system with a polytropic equation of state as a vanishing viscosity limit
• Limit of a consistent approximation to the complete compressible Euler System