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arXiv · 2111.14782

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

Claude Bardos·Trinh T. Nguyen·Toan T. Nguyen·Edriss S. Titi
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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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Claude Bardos, Trinh T. Nguyen, Toan T. Nguyen, Edriss S. Titi. 2021-11-29. The inviscid limit for the $2d$ Navier-Stokes equations in bounded domains. https://arxiv.org/abs/2111.14782

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