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

2019/10/30 by Wang, Fei
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.14449

Abstract

We consider the 3D Navier-Stokes equations in the upper half space \mathbb H³₊ with periodic boundary conditions in the horizontal directions. We prove the inviscid limit holds in the topology L^∞([0, T]; L²(\mathbb H³₊)) assuming the initial datum is analytic in the region \(x, y, z)∈\mathbb H³₊: 0≤ z≤ 1+μ₀\ for some positive μ₀ and has Sobolev regularity in the complement.

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