The surface tension makes free surfaces of fluids instantaneously smooth. For 2D gravity-capillary water 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 water waves in arbitrary dimensions. My main results are two propagation theorems for some quasi-homogeneous wavefront sets of gravity-capillary water waves. Speaker(s): Hui Zhu (University of Michigan)