Um estudo sobre soluções brandas para as equações de Navier-Stokes e Quase-geostrófica fracionárias

Abstract

This work studies the existence of a unique global in time mild solution for the 2D Quasi-geostrophic and 3D Navier-Stokes equations with critical fractional dissipation in Sobolev-Gevrey and Lei-Lin-Gevrey spaces, respectively. Furthermore, we establish some decay rates for the quasi-geostrophic case and local in time mild solutions for the Navier-Stokes system with subcritical fractional dissipation, in these same spaces cited previously. It is important to point out that the techniques applied in this research are related to Fourier Analysis, the use of Fixed Point Theorem and the behavior of the solutions for the Heat equation associated to these problems.