Global wellposedness of an inviscid \(2D\) Boussinesq system with nonlinear thermal diffusivity. (English) Zbl 1302.35319

Li, Dong; Xu, Xiaojing

Dyn. Partial Differ. Equ. 10, No. 3, 255-265 (2013).

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.

Reviewer: Titus Petrila (Cluj-Napoca)

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