Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data

Details Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data

2008-06-25

arxiv.org/abs/0806.4081v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

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. None smallness conditions are imposed on the data. The global existence issues for infinite energy initial velocity, and for the B\'enard system are also discussed.

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