Navier–Stokes equations: local existence, uniqueness and blow-up of solutions in Sobolev–Gevrey spaces

Abstract

ABSTRACT This work establishes local existence and uniqueness as well as blow-up criteria for solutions of the Navier–Stokes equations in Sobolev–Gevrey spaces . More precisely, if it is assumed that the initial data belongs to , with , we prove that there is a time T>0 such that for and . If the maximal time interval of existence of solutions is finite, , then, we prove, for example, that the blow-up inequality holds for , a>0, ( is the integer part of ).