Optimal control of the primitive equations of the ocean with state constraints

We investigate in this article 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 (2002) [7] for the three-dimensional Navier–Stokes (NS) equations. The main difference between this work and Wang (2002) [7] is that the nonlinearity in the PEs is stronger than in the three-dimensional NS systems.