On analyticity up to the boundary for critical quasi-geostrophic equations

2021/03/24 by Tsukasa Iwabuchi, Iwabuchi, Tsukasa
Mathematics · #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.2103.13005

17 pages

arxiv created 2021/09/14 · arxiv updated 2021/09/15

Abstract

We study the Cauchy problem for the quasi-geostrophic equations with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition. We show the global existence, the uniqueness and the analyticity of solutions, and the real analyticity up to the boundary is obtained. We will show one of natural ways to estimate the nonlinear term for functions satisfying the Dirichlet boundary condition.

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