Splash singularity for water waves.
basic_science · Level V
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- Record sourced from PubMed, PMID 22219372.
- Also identified by DOI 10.1073/pnas.1115948108 and PMC identifier 3271900.
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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.