Pontryagin’s maximum principle for optimal control of the stationary primitive equations of the ocean

We study in this article Pontryagin’s maximum principle for a class of control problems associated with the stationary primitive equations (PEs) of the ocean. These optimal problems involve a state constraint similar to that considered in [G. Wang, Pontryagin’s maximum principle for optimal control of the stationary Navier–Stokes equations, Nonlinear Anal. 52 (2003) 1853–1866] in the case of the three-dimensional Navier–Stokes (NS) equations. The main difference between this work and the one cited above is that the nonlinearity in PEs is stronger than that in the three-dimensional NS equations.