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 -symmetry.
@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}, mrnumber = {2240184}, zbl = {1105.35073}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2006_5_5_1_77_0/} }
TY - JOUR AU - Bodea, Simina TI - The motion of a fluid in an open channel JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 77 EP - 105 VL - 5 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2006_5_5_1_77_0/ LA - en ID - ASNSP_2006_5_5_1_77_0 ER -
Bodea, Simina. The motion of a fluid in an open channel. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 1, pp. 77-105. http://archive.numdam.org/item/ASNSP_2006_5_5_1_77_0/
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