Finite time singularities for water waves with surface tension. (English) Zbl 1328.76012
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}
©2012 American Institute of Physics}
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 |
References:
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