Caso supercrítico da equação quase-geostrófica

Abstract

In general, the Navier-Stokes equations describe the fluid dynamics. In this sense, these same equations represent models capable of expressing some physical laws in a mathematical way. Thereby, we highlight the equation of motion that determine the dynamics of geophysical fluids, which we call quasi-geostrophic equation. In this work, we investigate the existence and uniqueness of a global solution for this equation, with supercritical dissipation, in a specific usual non-homogeneous Sobolev space. Furthermore, we established the decay of this same solution, as time goes to infinity. It is important to point out that to obtain this global solution it is necessary to establish an blow-up criterion obtained for local solutions. For this purpose, we have used techniques related to Fourier Analysis.