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

Article type: Research Article

Authors: Cappiello, Marco^; | Nicola, Fabio

Affiliations: Dipartimento di Matematica, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy. E-mail: [email protected] | Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy. E-mail: [email protected]

Note: [] Corresponding author. E-mail: [email protected]

Abstract: We consider the Euler equations on Td with analytic data and prove lower bounds for the radius of spatial analyticity ε(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 ε(t) on the radius of analyticity of the initial datum.

Keywords: Euler equations, radius of analyticity

DOI: 10.3233/ASY-141260

Journal: Asymptotic Analysis, vol. 91, no. 2, pp. 103-110, 2015