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The hydrostatic approximation of the incompressible 3D stationary Navier Stokes équa- tions is widely used m oceanography and other apphed sciences It appears through a limit process due to the anisotropy of the domam in use, an océan, and it is usually studied as such We consider m this paper an equivalent formulation to this hydrostatic approximation that mcludes Coriohs force and an additional pressure tetm that comes from takmg into account the pressure in the state équation for the density It therefore models a shght dependence of the density upon compression terms We study this model as an independent mathematical object and prove an existence theorem by means of a mixed variational formulation The proof uses a family of finite element spaces to discretize the prob- lem coupled with a limit piocess that yields the solution We finish this papei with an existence and umqueness resuit foi the evolutionaiy lmeai pioblem associated to this model This pioblem mcludes the same additional pressuie teim and Coriohs force

Analysis of the hydrostatic approximation in oceanography with compression term