Asymptotic study of a global solution of super-critical Quasi-Geostrophic equation

2021/02/24 by Chaala Katar, Katar, Chaala
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2102.12265

openalex publication_date 2021/02/24 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the super-critical Quasi-Geostrophic equation in Gevrey-Sobolev space. We prove the local existence of (QG) for any large initial data and we give an exponential type of Blow-up to the solution. Moreover, we establish the existence global for a small initial data and we show that ‖θ‖_H^s_{a, α^-1} decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.

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