no. 1
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 
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     title = {The motion of a fluid in an open channel},
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     publisher = {Scuola Normale Superiore, Pisa},
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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. https://www.numdam.org/item/ASNSP_2006_5_5_1_77_0/

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