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

Structural stability for the splash singularities of the water waves problem

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

Mathematics

Research output: Contribution to journal › Article › peer-review

10 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 language	English (US)
Pages (from-to)	4997-5043
Number of pages	47
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	34
Issue number	12
DOIs	https://doi.org/10.3934/dcds.2014.34.4997
State	Published - 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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10.3934/dcds.2014.34.4997

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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 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.",

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AU - Castro, Angel

AU - Córdoba, Diego

AU - Fefferman, Charles

AU - Gancedo, Francisco

AU - Gómez-Serrano, Javier

PY - 2014/12

Y1 - 2014/12

N2 - 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.

AB - 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.

KW - Computer-assisted

KW - Contour dynamics

KW - Euler equation

KW - Splash singularity

KW - Water waves

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JF - Discrete and Continuous Dynamical Systems- Series A

IS - 12

ER -

Structural stability for the splash singularities of the water waves problem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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