Differential and Integral Equations

On the long time behaviour of the solution to the two-fluids incompressible Navier-Stokes equations

J.-F. Gerbeau and C. Le Bris

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Abstract

We devote this work to the long time behaviour of the solution to the incompressible Navier-Stokes equations for two viscous immiscible fluids contained in a bounded domain and subjected only to gravity forces. When there is surface tension at the interface or not, for the model linearized around the steady-state of minimal energy or for the standard nonlinear model, we investigate the following question. Do the equations reproduce the behaviour expected from experiment, namely a convergence to zero of the velocity field, and a convergence of the interface to its stable position. Our results show a wide variety of behaviours, depending on the case considered.

Article information

Source
Differential Integral Equations, Volume 12, Number 5 (1999), 691-740.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367255391

Mathematical Reviews number (MathSciNet)
MR1697251

Zentralblatt MATH identifier
1022.35038

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Gerbeau, J.-F.; Le Bris, C. On the long time behaviour of the solution to the two-fluids incompressible Navier-Stokes equations. Differential Integral Equations 12 (1999), no. 5, 691--740. https://projecteuclid.org/euclid.die/1367255391


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