The inviscid limit for the $2d$ Navier-Stokes equations in bounded domains
Analysis of PDEs
2021-11-30 v1
Abstract
We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary.
Keywords
Cite
@article{arxiv.2111.14782,
title = {The inviscid limit for the $2d$ Navier-Stokes equations in bounded domains},
author = {Claude Bardos and Trinh T. Nguyen and Toan T. Nguyen and Edriss S. Titi},
journal= {arXiv preprint arXiv:2111.14782},
year = {2021}
}
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28 pages