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

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.

arXiv admin note: text overlap with arXiv:1904.04983

References in corpus (1)

• On the zero-viscosity limit of the Navier-Stokes equations in the half-space

Cited by in corpus (1)

• Incompressible Euler limit from Boltzmann equation with Diffuse Boundary Condition for Analytic data