Asymptotic study of supercritical surface Quasi-Geostrophic equation in critical space. (November 2022)

• Record Type: Journal Article
• Authors: Benameur, Jamel; Katar, Chaala
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: 35-XX -- 35B44 -- 35Q30; Super-critical Quasi-Geostrophic equation -- Critical spaces -- Long time decay; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113074
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove, if θ ∈ C ( [ 0, ∞ ), H 2 − 2 α ( R 2 ) ) is a global solution of supercritical surface Quasi-Geostrophic equation with small initial data, then ‖ θ ( t ) ‖ H 2 − 2 α decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.