Structural stability for the splash singularities of the water waves problem

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

Research output: Contribution to journalArticle

5 Scopus citations

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 wave whose 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.

Original languageEnglish (US)
Pages (from-to)4997-5043
Number of pages47
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume34
Issue number12
DOIs
StatePublished - Dec 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Computer-assisted
  • Contour dynamics
  • Euler equation
  • Splash singularity
  • Water waves

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