Francisco Manuel Guillén González

An intrinsic analysis of existence of solutions for the hydrostatic approximation of Navier–Stokes equations

Abstract We prove an existence result for the hydrostatic approximations of Navier–Stokes equations, also called Primitive Equations of the Ocean. We perform a direct analysis of existence of solutions, which is not based upon a singular limit process. Our analysis is essentially based upon the existence of a reduced inf-sup condition for (3D) horizontal velocities and (2D) surface pressures. It applies to general domains, without the need of a boundary talus. Our existence result is, at the same time, a result of approximation by mixed finite elements.

The Cauchy problem and decay rates for strong solutions of a Boussinesq system

The Boussinesq equations describe the motion of an incompressible viscous fluid subject to convective heat transfer. Decay rates of derivatives of solutions of the three-dimension-al Cauchy problem for a Boussinesq system are studied in this work.