An alternative approach to global regularity for the 2D Euler–Boussinesq equations with critical dissipation. (January 2020)

• Record Type: Journal Article
• Authors: Ye, Zhuan
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35Q35 -- 35B65 -- 76D03; Boussinesq equations -- Global regularity; 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.2019.111591
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The purpose of this paper is to provide an alternative approach to the global regularity for the two-dimensional Euler–Boussinesq equations which couple the incompressible Euler equation for the velocity and a transport equation with fractional critical diffusion for the temperature. In contrast to the first proof of this result in [T. Hmidi, S. Keraani, and F. Rousset, Comm. Partial Differential Equations, 36 (2011), pp. 420–445] that took fully exploit of the hidden structure of the coupling system, the main argument in this manuscript is mainly based on the differentiability of the drift–diffusion equation.