The motion of a fluid in an open channel

Simina Bodea

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 1, page 77-105
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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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 5.1 (2006): 77-105. <http://eudml.org/doc/241419>.

@article{Bodea2006,
abstract = {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 $\{\mathbb \{Z\}\}_k$-symmetry.},
author = {Bodea, Simina},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Navier-Stokes equations; oscillations; existence; periodic solutions; spectral analysis; Hopf bifurcation},
language = {eng},
number = {1},
pages = {77-105},
publisher = {Scuola Normale Superiore, Pisa},
title = {The motion of a fluid in an open channel},
url = {http://eudml.org/doc/241419},
volume = {5},
year = {2006},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 1
SP - 77
EP - 105
AB - 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 ${\mathbb {Z}}_k$-symmetry.
LA - eng
KW - Navier-Stokes equations; oscillations; existence; periodic solutions; spectral analysis; Hopf bifurcation
UR - http://eudml.org/doc/241419
ER -

References

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  10. [10] B. Schweizer, Free boundary fluid systems in a semigroup approach and oscillatory behavior, SIAM J. Math. Anal. 28 (1997), 1135–1157. Zbl0889.35075MR1466673
  11. [11] B. Schweizer, A well-posed model for dynamic contact angles, Nonlinear Anal. 43 (2001), 109–125. Zbl0974.35095MR1784449
  12. [12] J. Socolowsky, The solvability of a free boundary value problem for the stationary Navier-Stokes equations with a dynamic contact line, Nonlinear Anal. 21 (1993), 763–784. Zbl0853.35134MR1246506
  13. [13] V. A. Solonnikov, On some free boundary problems for the Navier-Stokes equations with moving contact points and lines, Math. Ann. 302 (1995), 743–772. Zbl0926.35116MR1343648
  14. [14] V. A. Solonnikov, Solvability of two dimensional free boundary value problem for the Navier-Stokes equations for limiting values of contact angle, In: “Recent Developments in Partial Differential Equations”. Rome: Aracne. Quad. Mat. 2, 1998, 163–210. Zbl0932.35161MR1688371
  15. [15] R. Temam“Navier-Stokes Equations”, North-Holland, Amsterdam, 1977. Zbl0383.35057

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