Harmonic Analysis and Differential Equations Student Seminar: Propagation of singularities for gravity-capillary waves

Seminar | December 3 | 3:30-5 p.m. | 740 Evans Hall

 Hui Zhu, MSRI

 Department of Mathematics

The surface tension makes free surfaces of fluids instantaneously smooth. For 2D gravity-capillary waves, this phenomenon has been justified by Christianson–Hur–Staffilani and Alazard–Burq–Zuily as local smoothing effects. In this talk, I will present a microlocal justification of this phenomenon for gravity-capillary waves in arbitrary dimensions. My main results are two propagation theorems for some quasi-homogeneous wavefront sets of gravity-capillary waves.