Global well-posedness for the 2D Euler-Boussinesq-Bénard equations with critical dissipation. (English) Zbl 07825940
Summary: This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-Bénard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical dissipation for the temperature. We show that there is a global unique solution to this model with Yudovich’s type data. This settles the global regularity problem which was remarked by G. Wu and L. Xue [J. Differ. Equations 253, No. 1, 100–125 (2012; Zbl 1305.35119)].
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35R11 | Fractional partial differential equations |
| 76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
Keywords:
Bénard equations; Boussinesq equations; global regularity; uniqueness; Yudovich’s type dataCitations:
Zbl 1305.35119References:
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