Finite time singularities for water waves with surface tension

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

doi:10.1063/1.4765339

Finite time singularities for water waves with surface tension

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

Mathematics

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

23 Scopus citations

Abstract

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e., the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.

Original language	English (US)
Article number	115622
Journal	Journal of Mathematical Physics
Volume	53
Issue number	11
DOIs	https://doi.org/10.1063/1.4765339
State	Published - Nov 27 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4765339

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title = "Finite time singularities for water waves with surface tension",

abstract = "Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e., the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.",

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

note = "Funding Information: A.C., D.C., F.G., and J.G.S. were partially supported by the Grant No. MTM2011-26696 of the MCINN (Spain) and the Grant No. StG-203138CDSIF of the ERC. F.G. acknowledges support from the Ram{\'o}n y Cajal program. C.F. was partially supported by NSF Grant No. DMS-0901040. We are grateful for the support of the Fundaci{\'o}n General del CSIC.",

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T1 - Finite time singularities for water waves with surface tension

AU - Castro, Angel

AU - Córdoba, Diego

AU - Fefferman, Charles

AU - Gancedo, Francisco

AU - Gómez-Serrano, Javier

N1 - Funding Information: A.C., D.C., F.G., and J.G.S. were partially supported by the Grant No. MTM2011-26696 of the MCINN (Spain) and the Grant No. StG-203138CDSIF of the ERC. F.G. acknowledges support from the Ramón y Cajal program. C.F. was partially supported by NSF Grant No. DMS-0901040. We are grateful for the support of the Fundación General del CSIC.

PY - 2012/11/27

Y1 - 2012/11/27

N2 - Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e., the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.

AB - Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e., the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.

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Finite time singularities for water waves with surface tension

Abstract

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