The Three-Dimensional Inviscid Limit Problem with Data Analytic Near the Boundary

Abstract

We consider the three-dimensional 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.

Topics & Concepts