A Kato-Type Criterion for the Inviscid Limit of the Compressible Navier–Stokes System

We study the inviscid limit of the compressible Navier–Stokes system with no-slip boundary condition in a smooth bounded domain Ω⊆R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \subseteq {\mathbb {R}}^{2}$$\end{document}. Inspired by the work of (Sueur in J Math Fluid Mech 16:163–178, 2014; Constantin et al. in Proc Am Math Soc 143:3075–3090, 2015), we obtain a sufficient condition for the convergence of the solution of the compressible Navier–Stokes equations to the solution of the compressible Euler equations in the energy space L2(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}(\Omega )$$\end{document} uniformly in time.