In this talk, we will first review some recent results on local and global well-posedness of strong solutions to two dimensional nonhomogeneous incompressible primitive equations with constant viscosity. Then we will present local and global strong solutions to the two-dimensional nonhomogeneous incompressible primitive equations with density dependent viscosity. In our results, the initial vacuum is permitted.

Nonhomogeneous primitive equations, Local and global well-posedness, Strong solutions, Density-dependent viscosity