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.