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Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary by Chao Wang

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1Local Well-posedness And Break-down Criterion Of The Incompressible Euler Equations With Free Boundary

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In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschtiz function and the free surface belongs to $C^{\f32+\varepsilon}$. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.

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  • Title: ➤  Local Well-posedness And Break-down Criterion Of The Incompressible Euler Equations With Free Boundary
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  • Language: English

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