Abstract
Abstract
We adapt methodology of Tosio Kato to establish necessary and sufficient conditions for the solutions to the Navier–Stokes equations with Dirichlet boundary conditions to converge in a strong sense to a solution to the Euler equations in the presence of a boundary as the viscosity is taken to zero. We extend existing conditions for no-slip boundary conditions to allow for nonhomogeneous Dirichlet boundary conditions and curved boundaries, establishing several new conditions as well. We give a brief comparison of various correctors appearing in the literature used for similar purposes.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Reference66 articles.
1. Remarks in the inviscid limit for the compressible flows;Bardos,2016
2. The inviscid limit for the 2D Navier–Stokes equations in bounded domains;Bardos;Kinet. Relat. Models,2022
3. On the equations rot v = g and div u = f with zero boundary conditions;Borchers;Hokkaido Math. J.,1990