Lanterna Rally

Author: Chao Wang

Publisher: American Mathematical Soc.

Published: 2021-07-21

Total Pages: 119

ISBN-13: 1470446898

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.