On The Radius Of Analyticity Of Solutions To Semi-Linear Parabolic Systems

Jean-Yves Chemin (1) , Isabelle Gallagher (2, 3) , Ping Zhang (4)

1 LJLL - Laboratoire Jacques-Louis Lions
2 UPD7 - Université Paris Diderot - Paris 7
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 Institute of Automatic Control and Complex 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 = ∞, 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 ∈ C([0, ∞); H 1 2 (R 3)) of the Navier-Stokes equations, there holds lim inf t→∞ R(t)t − 1 2 = ∞.

Mots clés: Semi-linear parabolic systems; Radius of analyticity; Navier-Stokes equations AMS Subject Classification (2000): 35K55

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Yves Chemin, Isabelle Gallagher, Ping Zhang. On The Radius Of Analyticity Of Solutions To Semi-Linear Parabolic Systems. Mathematical Research Letters, 2020. ⟨hal-02537907⟩