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A Free Boundary Approach to Two-Dimensional Steady Capillary Gravity Water Waves
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Journal Article
A Free Boundary Approach to Two-Dimensional Steady Capillary Gravity Water Waves
2012
Overview
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.
Publisher
Springer-Verlag,Springer Nature B.V
