An alternative approach to global regularity for the 2D Euler-Boussinesq equations with critical dissipation

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. (C) 2019 Elsevier Ltd. All rights reserved.