Some remarks on the radius of spatial analyticity for the Euler equations

Abstract

We consider the Euler equations on ${\mathbb{T}}^d$ with analytic data and prove lower bounds for the radius of spatial analyticity $\epsilon (t)$ of the solution using a new method based on inductive estimates in standard Sobolev spaces. Our results are consistent with similar previous results proved by Kukavica and Vicol, but give a more precise dependence of $\epsilon (t)$ on the radius of analyticity of the initial datum.

Some misprints corrected