Long time existence of classical solutions for the 3D incompressible rotating Euler equations

Abstract

We consider the initial value problem of the 3D incompressible rotating Euler equations. We prove the long time existence of classical solutions for initial data in $H^s(\mathbb{R}^3)$ with $s$ > 5/2. Also, we give an upper bound of the minimum speed of rotation for the long time existence when initial data belong to $H^{7/2}(\mathbb{R}^3)$.