## Long time existence of classical solutions for the 3D incompressible rotating Euler equations.(English)Zbl 1338.35346

Summary: 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 $$H^{7/2}(\mathbb{R}^3)$$.

### MSC:

 35Q31 Euler equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 76U05 General theory of rotating fluids 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids

### Keywords:

3D Euler equations; Coriolis force; long time existence
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### References:

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