Global existence of a solution to the ocean dynamics equations

The problem of proving the existence and uniqueness of a solution to the system of equations describing the ocean dynamics was investigated. The existence theorems were proved only for a local solution or for a global solution under the assumption that the domain or initial data are small. A case of Cartesian coordinate system and a zero right-hand side with the heat and salinity equations replaced by a single one, but the reasoning remains valid for the general system of equations. The proof of the existence of a global solution to problem is based on a sequence of a priori estimates.