no. 4
Global bifurcation theory for periodic traveling interfacial gravity–capillary waves
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1081-1101.

We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity–capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can be positive, negative, or zero, and the surface tension parameter is positive. Thus, included in the parameter set are the cases of pure capillary water waves and gravity–capillary water waves. Our choice of coordinates allows for the possibility that the fluid interface is not a graph over the horizontal. We use a technical reformulation which converts the traveling wave equations into a system of the form “identity plus compact.” Rabinowitz' global bifurcation theorem is applied and the final conclusion is the existence of either a closed loop of solutions, or an unbounded set of nontrivial traveling wave solutions which contains waves which may move arbitrarily fast, become arbitrarily long, form singularities in the vorticity or curvature, or whose interfaces self-intersect.

DOI : 10.1016/j.anihpc.2015.03.005
Mots clés : Global bifurcation, Surface tension, Traveling wave, Interfacial flow, Water wave 
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     title = {Global bifurcation theory for periodic traveling interfacial gravity{\textendash}capillary waves},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Ambrose, David M.; Strauss, Walter A.; Wright, J. Douglas. Global bifurcation theory for periodic traveling interfacial gravity–capillary waves. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1081-1101. doi : 10.1016/j.anihpc.2015.03.005. http://www.numdam.org/articles/10.1016/j.anihpc.2015.03.005/

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