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| In this talk, 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 $s>5/2$ provided the speed of rotation is sufficiently high. Also, we give an upper bound of the minimum rotating speed for the long time existence when initial data belong to $H^{\frac{7}{2}}(\mathbb{R}^3)$. |
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