English

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}
}

Comments

28 pages