Solvability of primitive equations for the ocean with vertical mixing

Abstract

Small time existence of a strong solution to the free surface problem of primitive equations for the ocean with the variable turbulent viscosity terms is shown in this paper. The turbulent viscosity coefficients, which include the Richardson number depending on the unknown variables, are formulated explicitly. We consider the problem in the 3-dimensional stripe-like region, and construct the strong local-in-time solution in Sobolev-Slobodetskiĭ spaces. The details of the proofs will be provided in another full paper.