Open AccessOn analyticity up to the boundary for critical quasi-geostrophic equation in the half space
Author(s) -
Tsukasa Iwabuchi
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2022016
Subject(s) - dirichlet boundary condition , boundary value problem , mathematical analysis , mathematics , uniqueness , cauchy boundary condition , geostrophic wind , space (punctuation) , nonlinear system , boundary (topology) , half space , physics , computer science , quantum mechanics , mechanics , operating system
We study the Cauchy problem for the surface quasi-geostrophic equation 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 a natural ways to estimate the nonlinear term for functions satisfying the Dirichlet boundary condition.