Splash singularity for water waves.

ABSTRACT: 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.

SUBMITTER: Castro A 

PROVIDER: S-EPMC3271900 | biostudies-literature | 2012 Jan

REPOSITORIES: biostudies-literature