Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data

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.

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