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

2020/04/08 by Jean-Yves Chemin, Isabelle Gallagher, Chemin, Jean-Yves +3
Mathematics · #35K55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.03908

openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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^-\frac12 is bounded from below by a positive constant. In this paper we prove that~\liminf_{t→ 0} R(t)t^-\frac12= ∞, 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^\frac12(\R³)) of the Navier-Stokes equations, there holds~\liminf_{t→ ∞} R(t)t^-\frac12= ∞.

Citations

• Gevrey class regularity for the solutions of the Navier-Stokes equations

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