Text only print
Full screen print
Lectures
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
2011/02/02
15:15-16:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Guanghui ZHANG (Graduate School of Mathematical Sciences, the University of Tokyo)
Regularity of two dimensional capillary gravity water waves (ENGLISH)
Guanghui ZHANG (Graduate School of Mathematical Sciences, the University of Tokyo)
Regularity of two dimensional capillary gravity water waves (ENGLISH)
[ Abstract ]
We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem 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. This is a joint work with Georg Weiss.
We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem 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. This is a joint work with Georg Weiss.
