On the existence and uniqueness of classical global solution to a type of Boussinesq equations

The existence and uniqueness of classical global solutions to a type of Boussinesq equations with initial and boundary values are studied in this paper. The existence of such solutions is proved by means of compactness theorem and Schauders fixed point theorem, and its uniqueness by the so called energy method.Projects Supported by the Science Fund of the Chinese Academy of Sciences.