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An alternative approach to global regularity for the 2D Euler-Boussinesq equations with critical dissipation. (English) Zbl 1431.35142
Summary: 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 et al., Commun. Partial Differ. Equations 36, No. 1–3, 420–445 (2011; Zbl 1284.76089)] 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.
35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35R11 Fractional partial differential equations
Full Text: DOI
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