Voir la notice de l'article provenant de la source Numdam
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.
@article{AIHPC_2016__33_4_1081_0,
author = {Ambrose, David M. and Strauss, Walter A. and Wright, J. Douglas},
title = {Global bifurcation theory for periodic traveling interfacial gravity{\textendash}capillary waves},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1081--1101},
publisher = {Elsevier},
volume = {33},
number = {4},
year = {2016},
doi = {10.1016/j.anihpc.2015.03.005},
zbl = {1383.35145},
mrnumber = {3519533},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.03.005/}
}
TY - JOUR AU - Ambrose, David M. AU - Strauss, Walter A. AU - Wright, J. Douglas TI - Global bifurcation theory for periodic traveling interfacial gravity–capillary waves JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1081 EP - 1101 VL - 33 IS - 4 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.03.005/ DO - 10.1016/j.anihpc.2015.03.005 LA - en ID - AIHPC_2016__33_4_1081_0 ER -
%0 Journal Article %A Ambrose, David M. %A Strauss, Walter A. %A Wright, J. Douglas %T Global bifurcation theory for periodic traveling interfacial gravity–capillary waves %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1081-1101 %V 33 %N 4 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.03.005/ %R 10.1016/j.anihpc.2015.03.005 %G en %F AIHPC_2016__33_4_1081_0
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
Cité par Sources :