Splash singularity for water waves.
We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, Campus Cantoblanco, 28049 Madrid, Spain.
Angel
A
Castro
Diego
D
Córdoba
Charles L
CL
Fefferman
Francisco
F
Gancedo
Javier
J
Gómez-Serrano