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Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation. (English) Zbl 1452.76030
Summary: In this paper we consider the Yudovich type solution of the 2D inviscid Boussinesq system with critical and supercritical dissipation. For the critical case, we show that the system admits a global and unique Yudovich type solution; for the supercritical case, we prove the local and unique existence of Yudovich type solution, and the global result under a smallness condition of $${{\theta}_0}$$. We also give a refined blowup criterion in the supercritical case.

##### MSC:
 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids 35Q35 PDEs in connection with fluid mechanics 35B44 Blow-up in context of PDEs
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