Error estimates and existence of solutions for an atmospheric model of Lorenz on periodic domains Original Research Article

This paper deals with equations governing an atmospheric model of Lorenz derived from the incompressible f-plane shallow-water equations under a time independent mass forcing. The horizontal and vertical motions of the fluid are damped diffusively by coefficients ν and κ, where κ is taken to be a turbulent viscosity. For small initial data, we prove the existence of weak and strong solutions of such a problem. Uniqueness is proved only for strong solutions. Furthermore, we prove that the solutions to the system of equations of the approximating Galerkin problem converge to that of the original systems and error estimates are established.