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

Finite time singularities for water waves with surface tension. (English) Zbl 1328.76012

J. Math. Phys. 53, No. 11, 115622, 26 p. (2012).
Summary: 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. {
©2012 American Institute of Physics}

Cited in 18 Documents

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76D45 Capillarity (surface tension) for incompressible viscous fluids
35A20 Analyticity in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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References:

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