# On the existence of extreme waves and the Stokes conjecture with vorticity

@article{Varvaruca2007OnTE, title={On the existence of extreme waves and the Stokes conjecture with vorticity}, author={Eugen Varvaruca}, journal={Journal of Differential Equations}, year={2007}, volume={246}, pages={4043-4076} }

## 66 Citations

### Stokes waves with vorticity

- Mathematics
- 2009

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as…

### On Some Properties of Traveling Water Waves with Vorticity

- Mathematics, Environmental ScienceSIAM J. Math. Anal.
- 2008

We prove that for a large class of vorticity functions the crest of a corresponding travelling water wave is necessarily a point of maximal horizontal velocity. We also show that for waves with…

### Solitary water waves with discontinuous vorticity

- MathematicsJournal de Mathématiques Pures et Appliquées
- 2019

### On Rotational Waves of Limit Amplitude

- PhysicsFunctional Analysis and Its Applications
- 2021

Abstract In this note we discuss some recent results on extreme steady waves under gravity. They include the existence and regularity theorems for highest waves on finite depth with and without…

### Stokeswaves with vorticity

- Mathematics
- 2011

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep body of water under the force of gravity is established for a general class of vorticities.…

### Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation

- Mathematics
- 2011

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed…

### Periodic waves over constant vorticity: Some asymptotic results generated by parameter expansions

- Physics, Environmental Science
- 2009

### Global bifurcation and highest waves on water of finite depth

- Mathematics
- 2020

We consider the two-dimensional problem for steady water waves on finite depth with vorticity. While neglecting the effects of surface tension we construct connected families of large amplitude…

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We prove that for a large class of vorticity functions the crest of a corresponding travelling water wave is necessarily a point of maximal horizontal velocity. We also show that for waves with…

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The classical deep-water wave problem is to find a periodic traveling wave with a free surface of infinite depth. The main result is the construction of a global connected set of rotational solutions…

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Periodic waves propagating at a constant velocity at the surface of a fluid with constant vorticity in water of infinite depth are considered. The problem is solved numerically by a…

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We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two‐dimensional inviscid periodic…

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Abstract This paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the…

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It is shown that there exists a solution of Nekrasov’s integral equation which corresponds to the existence of a wave of greatest height and of permanent form moving on the surface of an…

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Two-dimensional steady surface waves on a shearing flow are computed for the special case where the flow has uniform vorticity, i.e. in the absence of waves the velocity varies linearly with height.…

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The behavior of steady, periodic, deep-water gravity waves on a linear shear current is investigated. A weakly nonlinear approximation for the small amplitude waves is constructed via a variational…

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Stokes conjectured in 1880 that an extreme gravity wave on water (or ‘wave of greatest height’) exists, has sharp crests of included angle 2π/3 and has a boundary that is convex between successive…