Communications in Mathematical Sciences
Volume 16 (2018)
On the 3D Euler equations with Coriolis force in borderline Besov spaces
Pages: 145 – 164
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.
Euler equations, Coriolis force, long-time solvability, blow up, Besov-spaces
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