Regularity criterion of the 2D Bénard equations with critical and supercritical dissipation. (June 2017)

• Record Type: Journal Article
• Authors: Ye, Zhuan
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 111
• Page End: 143
• Publication Date: 2017-06
• Subjects: 35Q35 -- 35B65 -- 76D03; Bénard equations -- Boussinesq equations -- Global regularity -- Regularity criterion; 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.2017.02.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we investigate the Cauchy problem for the two-dimensional (2D) incompressible Bénard equations. On the one hand, we prove global-in-time existence of smooth solutions to the 2D Bénard equations with critical dissipation. On the other hand, we establish several regularity criteria involving temperature for 2D Bénard equations with supercritical dissipation.