The 3D inviscid limit problem with data analytic near the boundary

Fei Wang

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arXiv · 1910.14449

The 3D inviscid limit problem with data analytic near the boundary

Fei Wang

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Abstract

We consider the 3D Navier-Stokes equations in the upper half space $\mathbb H^3_+$ with periodic boundary conditions in the horizontal directions. We prove the inviscid limit holds in the topology $L^\infty([0, T]; L^2(\mathbb H^3_+))$ assuming the initial datum is analytic in the region $\{(x, y, z)\in\mathbb H^3_+: 0\le z\le 1+\mu_0\}$ for some positive $\mu_0$ and has Sobolev regularity in the complement.

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Fei Wang. 2019-10-30. The 3D inviscid limit problem with data analytic near the boundary. https://arxiv.org/abs/1910.14449

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