A Free Boundary Approach to Two-Dimensional Steady Capillary Gravity Water Waves

作者:Weiss Georg S*; Zhang Guanghui
来源:Archive for Rational Mechanics and Analysis, 2012, 203(3): 747-768.
DOI:10.1007/s00205-011-0466-3

摘要

We prove that suitable weak solutions of the two-dimensional steady capillary gravity water wave problem (even in the presence of vorticity) are smooth. On a technical level, solutions are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. We prove that cusps do not exist, and that the free surface is smooth.

  • 出版日期2012-3