Angled crested like water waves with surface tension: Wellposedness of the problem

2019/09/20 by Agrawal, Siddhant
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.09671

Abstract

We consider the capillary-gravity water wave equation in two dimensions. We assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. We construct an energy functional and prove a local wellposedness result without assuming the Taylor sign condition. When the surface tension σ is zero, the energy reduces to a lower order version of the energy obtained by Kinsey and Wu [23] and allows angled crest interfaces. For positive surface tension, the energy does not allow angled crest interfaces but admits initial data with large curvature of the order of σ^{-(1)/(3) + ε} for any ε>0.

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