Asymptotic behavior of critical dissipative quasi-geostrophic equation in Fourier space

2020/03/29 by Jamel Benameur, Benameur, Jamel, Saber Ben Abdallah +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.2003.13143

arxiv created 2020/03/29 · openalex publication_date 2020/03/29 · arxiv updated 2020/03/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper we show the global existence for critical dissipative quasi-geostrophic equations if ‖\widehatθ⁰‖_L¹ is small enough; among others we prove the analyticity of such a solution. If in addition the initial condition verifies |D|^-δθ⁰∈ L¹(\mathbb R²) with 0<δ<1, then the solution remains regular and lim_t→∞t^δ‖\widehatθ(t)‖_L¹=0. Fourier analysis and standard techniques are used.

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