Maximum Principle of Optimal Control of the Primitive Equations of the Ocean With State Constraint

We investigate in this paper Pontryagin's maximum principle for a class of control problems associated with the primitive equations (PEs) of the ocean. These optimal problems involve a state constraint similar to that considered in Wang and Wang (Nonlinear Analysis 2003; 52:1911-1931) for the three-dimensional Navier-Stokes (NS) equations. The main difference between this work and Wang and Wang (Nonlinear Analysis 2003; 52:1911-1931) is that the nonlinearity in the PEs is stronger than in the three-dimensional NS systems.