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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
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