The 3D inviscid limit problem with data analytic near the boundary
Abstract
We consider the 3D NavierStokes 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.14449
 Bibcode:
 2019arXiv191014449W
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 arXiv admin note: text overlap with arXiv:1904.04983