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Global well-posedness for the 2D inviscid Bénard system with fractional diffusivity and Yudovich’s type data. (English) Zbl 1305.35119
Summary: We consider the Cauchy problem of the two-dimensional inviscid Bénard system with fractional diffusivity. We show that there is a global unique solution to this system with Yudovich’s type data.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35Q86 PDEs in connection with geophysics
35R11 Fractional partial differential equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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