Local well-posedness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscosity

In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility condition. The initial density does not need to be strictly positive and may contain vacuum. Meanwhile, we also give the corresponding blow-up criterion if the maximum existence interval with respect to the time is finite.