Splash singularity for water waves

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

doi:10.1073/pnas.1115948108

Splash singularity for water waves

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

Mathematics

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

32 Scopus citations

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.

Original language	English (US)
Pages (from-to)	733-738
Number of pages	6
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	109
Issue number	3
DOIs	https://doi.org/10.1073/pnas.1115948108
State	Published - Jan 17 2012

All Science Journal Classification (ASJC) codes

General

Keywords

Blow-up
Euler
Free boundary
Incompressible

Access to Document

10.1073/pnas.1115948108

Cite this

@article{bcbd92aaa2a1490298c9af410aae554f,

title = "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.",

keywords = "Blow-up, Euler, Free boundary, Incompressible",

author = "Angel Castro and Diego C{\'o}rdoba and Fefferman, \{Charles L.\} and Francisco Gancedo and Javier G{\'o}mez-Serrano",

year = "2012",

month = jan,

day = "17",

doi = "10.1073/pnas.1115948108",

language = "English (US)",

volume = "109",

pages = "733--738",

journal = "Proceedings of the National Academy of Sciences of the United States of America",

issn = "0027-8424",

publisher = "National Academy of Sciences",

number = "3",

}

TY - JOUR

T1 - Splash singularity for water waves

AU - Castro, Angel

AU - Córdoba, Diego

AU - Fefferman, Charles L.

AU - Gancedo, Francisco

AU - Gómez-Serrano, Javier

PY - 2012/1/17

Y1 - 2012/1/17

N2 - 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.

AB - 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.

KW - Blow-up

KW - Euler

KW - Free boundary

KW - Incompressible

UR - https://www.scopus.com/pages/publications/84856371495

UR - https://www.scopus.com/pages/publications/84856371495#tab=citedBy

U2 - 10.1073/pnas.1115948108

DO - 10.1073/pnas.1115948108

M3 - Article

C2 - 22219372

AN - SCOPUS:84856371495

SN - 0027-8424

VL - 109

SP - 733

EP - 738

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 3

ER -

Splash singularity for water waves

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this