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Global well-posedness issues for the inviscid Boussinesq system with Yudovich’s type data. (English) Zbl 1186.35157
Summary: The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption on the initial temperature, there exists a global unique solution. No smallness conditions are imposed on the data. The global existence issues for infinite energy initial velocity, and for the Bénard system are also discussed.

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
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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