The inviscid limit for the 2D Navier-Stokes equations in bounded domains

Claude W. Bardos; Trinh T. Nguyen; Toan T. Nguyen; Edriss S. Titi

doi:10.3934/krm.2022004

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2022, Volume 15, Issue 3: 317-340. Doi: 10.3934/krm.2022004

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The inviscid limit for the 2D Navier-Stokes equations in bounded domains

1.
Laboratoire J.-L. Lions, Sorbonne Université, 75252 Paris, Cedex 05, France
2.
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
3.
Department of Mathematics, Penn State University, State College, PA 16802, USA
4.
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
5.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
6.
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel

^* Corresponding author: Toan T. Nguyen
^* Corresponding author: Toan T. Nguyen

In memory of Robert T. Glassey

Received: November 2021

Early access: January 2022

Published: June 2022

The second author is partly supported by the AMS-Simons Travel Grant Award and the third author is supported by the NSF under grant DMS-2054726..

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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.

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Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 76D05, 76D10.

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References

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