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

  • * Corresponding author: Toan T. Nguyen

    * Corresponding author: Toan T. Nguyen 

In memory of Robert T. Glassey

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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  • 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.

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


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