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Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary
Chao Wang
出版American Mathematical Soc., 2021-07-21
主題Education / General
ISBN14704468989781470446895
URLhttp://books.google.com.hk/books?id=HvY8EAAAQBAJ&hl=&source=gbs_api
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註釋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 Lipschitz function and the free surface belongs to C 3 2 +ε. 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.