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Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity. (English) Zbl 1307.35214
The 2-D Boussinesq system is considered, related with an inviscid fluid and thermal diffusivity depending on the temperature. The main tools are: Littlewood-Paley decomposition and some Sobolev spaces. The Gagliardo-Nirenberg’s inequality is used to obtain a priori estimates. Friedrichs method is used to get the local well-posedness. The global well-posedness is obtained in the last part, by using the corresponding vorticity.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B45 A priori estimates in context of PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
42B25 Maximal functions, Littlewood-Paley theory
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