Existência de soluções clássicas para as equações de Burgers e Navier-Stokes

by Melo, Wilberclay Gonçalves

We study existence and uniqueness of classical solutions for the viscous Burgers equation, as well as for the Navier-Stokes system for viscous incompressible fluids, in both two and three space dimensions. We prove local existence of solutions in all cases. Moreover, global existence is shown for two dimensional Navier-Stokes and Burgers. We show why one does not get global solutions for the Navier-Stokes in thethree dimensional case