Structural stability for the splash singularities of the water waves problem

Angel Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; Javier Gómez-Serrano

doi:10.3934/dcds.2014.34.4997

Article Contents

2014, Volume 34, Issue 12: 4997-5043. Doi: 10.3934/dcds.2014.34.4997 open access

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Structural stability for the splash singularities of the water waves problem

1.
Departamento de Matemáticas de la UAM, Instituto de Ciencias Matemáticas del CSIC, Campus de Cantoblanco, 28049 Madrid
2.
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera, 13-15, 28049 Madrid
3.
Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Road, Princeton, New Jersey 08544
4.
Departamento de Análisis Matemático & IMUS, Universidad de Sevilla, Campus Reina Mercedes, 41012 Sevilla
5.
Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Rd, Princeton, NJ 08544

Received: December 31, 2013

Revised: April 30, 2014

Published: November 2014

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Abstract

In this paper we show a structural stability result for water waves. The main motivation for this result is that we aim to exhibit a water wavewhose interface starts as a graph and ends in a splash. Numerical simulations lead to an approximate solution with the desired behaviour. The stability result will conclude that near the approximate solution to water waves there is an exact solution.

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Mathematics Subject Classification: Primary: 76B15, 35Q31; Secondary: 76E09.

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References

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