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.
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