The motion of a fluid in an open channel
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 1, pp. 77-105.

We consider a free boundary value problem for a viscous, incompressible fluid contained in an uncovered three-dimensional rectangular channel, with gravity and surface tension, governed by the Navier-Stokes equations. We obtain existence results for the linear and nonlinear time-dependent problem. We analyse the qualitative behavior of the flow using tools of bifurcation theory. The main result is a Hopf bifurcation theorem with ${ℤ}_{k}$-symmetry.

Classification : 35Q30,  35P99
@article{ASNSP_2006_5_5_1_77_0,
author = {Bodea, Simina},
title = {The motion of a fluid in an open channel},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {77--105},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {1},
year = {2006},
zbl = {1105.35073},
mrnumber = {2240184},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2006_5_5_1_77_0/}
}
Bodea, Simina. The motion of a fluid in an open channel. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 1, pp. 77-105. http://www.numdam.org/item/ASNSP_2006_5_5_1_77_0/

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