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Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary

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arxiv 1507.02478 v1 pith:QAMRIP3Z submitted 2015-07-09 math.AP

Chao Wang , Zhifei Zhang , Weiren Zhao , Yunrui Zheng This is my paper · ORCID
classification math.AP
keywords freeboundarybreak-downcriterionequationseulerincompressiblelocal
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abstract

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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  1. The Euler equations with variable coefficients

    math.AP 2025-09 conditional novelty 7.0 of 10

    Local existence for variable-coefficient 3D Euler at optimal regularity r>2.5, plus a BKM blow-up criterion at r=3 involving BMO vorticity and H1 velocity.

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