Solvability of the altimeter data assimilation problem in the quasi-geostrophic multilayer model of ocean circulation (Q1974759)

The problem of variational data assimilation in the quasigeostrophic ocean circulation model is considered. Mathematical analysis of optimal control problems as applied to complex hydrodynamics models, which is the focus of this paper, cannot be performed without a preliminary development of solvability theory for these models. As a rule, the analysis employs appropriate regularization methods. It is proved that solutions can be found for positive values of the regularization parameter. The necessary optimality conditions are obtained.