Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary
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Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary
Author: Chao Wang
language: en
Publisher: American Mathematical Soc.
Release Date: 2021-07-21
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.
Elliptic Theory for Sets with Higher Co-Dimensional Boundaries
Author: Guy David
language: en
Publisher: American Mathematical Society
Release Date: 2021-12-30
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