Existence, uniqueness and blow-up of solutions for the 3D Navier–Stokes equations in homogeneous Sobolev–Gevrey spaces

Abstract

We show existence and uniqueness of solutions for the classical Navier–Stokes equations in Sobolev–Gevrey spaces $${\dot{H}}_{a,\sigma }^s(\mathbb {R}^3)$$, where $$s\in (1/2,3/2)$$, $$a>0$$ and $$\sigma \ge 1$$; furthermore, we present some blow-up criteria considering these same spaces with $$\sigma >1$$.