Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

On the 3D Euler equations with Coriolis force in borderline Besov spaces

Pages: 145 – 164

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n1.a7

Authors

Vladimir Angulo-Castillo (Departamento de Matemática, Universidade Estadual de Campinas, SP, Brazil)

Lucas C. F. Ferreira (Departamento de Matemática, Universidade Estadual de Campinas, SP, Brazil)

Abstract

We consider the 3D Euler equations with Coriolis force (EC) in the whole space. We show long-time solvability in Besov spaces for high speed of rotation $\Omega$ and arbitrary initial data. For that, we obtain $\Omega$-uniform estimates and a blow-up criterion of BKM type in our framework. Our initial data class is larger than previous ones considered for (EC) and covers borderline cases of the regularity. The uniqueness of solutions is also discussed.

Keywords

Euler equations, Coriolis force, long-time solvability, blow up, Besov-spaces

Full Text (PDF format)

The authors thank an anonymous referee for his/her comments and suggestions. V. Angulo-Castillo was supported by CNPq, Brazil. LCF Ferreira was supported by FAPESP and CNPq, Brazil.

Received 28 October 2016

Accepted 15 October 2017

Published 29 March 2018