2004 年 47 巻 2 号 p. 225-250
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.