Differential and Integral Equations
- Differential Integral Equations
- Volume 12, Number 5 (1999), 691-740.
On the long time behaviour of the solution to the two-fluids incompressible Navier-Stokes equations
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.
Differential Integral Equations, Volume 12, Number 5 (1999), 691-740.
First available in Project Euclid: 29 April 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 76D05: Navier-Stokes equations [See also 35Q30]
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