DEPARTAMENTO DE MATEMÁTICA – CFM / UFSC

In this talk, we consider the evolutive problem for the incompressible Navier–Stokes equations with a general diffusion which can be fully anisotropic. The existence of weak solutions is proved for the associated initial problem supplemented with no-slip boundary conditions. We prove also the properties of extinction in a finite time, exponential time decay and power time decay. With this respect, we consider the important case of a forces fields with possible different behavior in distinct directions. Perturbations of the asymptotically stable equilibrium are established as well. If time permits, we will also study the effect of an anisotropic damping term introduced in the momentum equation.