## On the Boussinesq flow with nondecaying initial data.(English)Zbl 1118.35037

Summary: This paper is concerned with the Boussinesq equations which describe the heat convection in a viscous incompressible fluid. Local existence and uniqueness theorems are established for the $$n$$-dimensional Boussinesq equations in the whole space with nondecaying initial data. In two dimensional case the solution can be extended globally in time without smallness of the initial data.

### MSC:

 35Q35 PDEs in connection with fluid mechanics 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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