Zero Viscosity Limit of Steady Compressible Shear Flow with Navier-Slip Boundary

2024/06/07 by Wenbin Li, Chun Hui Zhou, Li, Wenbin +1
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Navier-Stokes equation solutions #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.2406.04700

Abstract

We investigate the existence and the zero viscosity limit of steady compressible shear flow with Navier-slip boundary condition in the absence of any external force in a two-dimension domain Ω=(0,L)×(0,2). More precisely, under the assumption that the Mach number η<\va^\f12+ and L≪1, we prove the existence of smooth solutions to steady compressible Naiver-Stokes equations near plane Poiseuille-Couette flow as well as the convergence of the solutions obtained above to the solutions of steady incompressible Euler equations when the viscous \va tends to zero.

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