Local and global solvability for the Boussinesq system in Besov spaces

This article focuses on local and global existence and uniqueness for the strong solution to the Boussinesq system in ( ) with full viscosity in Besov spaces. Under the hypotheses and , and the initial condition , the Boussinesq system is proved to have a unique local strong solution. Under the hypotheses and , or especially and , and the initial condition with sufficiently small norms and , the Boussinesq system is proved to have a unique global strong solution.