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We prove the existence of small steady periodic capillary-gravity water waves for stratified flows, where we allow for stagnation points in the flow. We establish the existence of both laminar and non-laminar flow solutions for the governing equations. This is achieved using bifurcation theory and estimates based on the ellipticity of the system, where we regard, in turn, the mass-flux and surface tension as bifurcation parameters.
@article{ASNSP_2013_5_12_4_955_0,
author = {Henry, David and Matioc, Bogdan-Vasile},
title = {On the existence of steady periodic capillary-gravity stratified water waves},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {955--974},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 12},
number = {4},
year = {2013},
mrnumber = {3184575},
zbl = {1290.35201},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_955_0/}
}
TY - JOUR AU - Henry, David AU - Matioc, Bogdan-Vasile TI - On the existence of steady periodic capillary-gravity stratified water waves JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2013 SP - 955 EP - 974 VL - 12 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_955_0/ LA - en ID - ASNSP_2013_5_12_4_955_0 ER -
%0 Journal Article %A Henry, David %A Matioc, Bogdan-Vasile %T On the existence of steady periodic capillary-gravity stratified water waves %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2013 %P 955-974 %V 12 %N 4 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_955_0/ %G en %F ASNSP_2013_5_12_4_955_0
Henry, David; Matioc, Bogdan-Vasile. On the existence of steady periodic capillary-gravity stratified water waves. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 955-974. http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_4_955_0/