Global bifurcation of steady gravity water waves with critical layers

2014/07/01 by Constantin, Adrian, Strauss, Walter, Varvaruca, Eugen · 10 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.0092

Abstract

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 used to recast the governing equations as a one-dimensional elliptic pseudo-differential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler-Lagrange equation of an energy functional, enable us to develop a theory of analytic global bifurcation.

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