The Stokes conjecture for waves with vorticity

Varvaruca, E. and Weiss, G. S. (2012) The Stokes conjecture for waves with vorticity. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 29 (6). pp. 861-885. ISSN 0294-1449 doi: 10.1016/j.anihpc.2012.05.001

Abstract/Summary

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/27574
Identification Number/DOI	10.1016/j.anihpc.2012.05.001
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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