Remarks on the inviscid limit for the compressible flows

2014/10/18 by Claude Bardos, Bardos, Claude, Toan T. Nguyen +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1410.4952

openalex publication_date 2014/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish various criteria, which are known in the incompressible case, for the validity of the inviscid limit for the compressible Navier-Stokes flows considered in a general domain Ω in ℝⁿ with or without a boundary. In the presence of a boundary, a generalized Navier boundary condition for velocity is assumed, which in particular by convention includes the classical no-slip boundary conditions. In this general setting we extend the Kato criteria and show the convergence to a solution which is dissipative "up to the boundary". In the case of smooth solutions, the convergence is obtained in the relative energy norm.

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