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Global wellposedness of an inviscid $$2D$$ Boussinesq system with nonlinear thermal diffusivity. (English) Zbl 1302.35319
The authors consider a two-dimensional inviscid Boussinesq system with temperature-dependent thermal diffusivity. They prove global wellposedness of strong solutions for arbitrarily large initial data in Sobolev spaces. For this target a global regularity result (Theorem 1.3) is proved. This is backed on another result obtained by Ch. Wang and Zh. Zhang [Adv. Math. 228, No. 1, 43–62 (2011; Zbl 1231.35180)] re-obtained by the authors of this note in a simplified way.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
##### Keywords:
Boussinesq system; global wellposedness; Sobolev spaces
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