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

• Adrian Constantin, Eugen Varvaruca
• 2009

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… (More)

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

• Eugen Varvaruca
• 2008

This 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… (More)

Global Bifurcation of Steady Gravity Water Waves with Critical Layers

• Adrian Constantin, Eugen Varvaruca
• 2014

We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is… (More)

Equivalence of weak formulations of the steady water waves equations.

• Eugen Varvaruca, Arghir D Zarnescu
• Philosophical transactions. Series A…
• 2012

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under… (More)

On Some Properties of Traveling Water Waves with Vorticity

• Eugen Varvaruca
• SIAM J. Math. Analysis
• 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… (More)

A Geometric Approach to Generalized Stokes Conjectures

• Eugen Varvaruca
• 2009

Abstract. We consider Stokes’ conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes’ conjecture… (More)

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