Global Wellposedness of the Primitive Equations with Nonlinear Equation of State in Critical Spaces

This article investigates the primitive equations with nonlinear equations of state. A global, strong well-posedness result for this set of equations is established for initial data lying in critical spaces provided that the density, depending on temperature, salinity and pressure, satisfies certain regularity assumptions. These assumptions are in particular satisfied for the TEOS-80 formulation of the equation of state.