On the existence of extreme waves and the Stokes conjecture with vorticityVarvaruca, E. (2009) On the existence of extreme waves and the Stokes conjecture with vorticity. Journal of Differential Equations, 246 (10). pp. 4043-4076. ISSN 0022-0396 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.jde.2008.12.018 Abstract/SummaryThis is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.
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