On the radius of analyticity of solutions to semi-linear parabolic systems

We study the radius of analyticity R(t) in space, of strong solutions to systems of scale-invariant semi-linear parabolic equations. It is well-known that near the initial time, R(t)t(-1/2) is bounded from below by a positive constant. In this paper we prove that lim inf(t -> 0) R(t)t(-1/2) = infinity, and assuming higher regularity for the initial data, we obtain an improved lower bound near time zero. As an application, we prove that for any global solution u in C ([0,8); H-1/2 (R-3)) of the Navier-Stokes equations, there holds lim inf(t -> 0) R(t)t(-1/2) = infinity.