Abstract
Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered. They consist of the 3D incompressible Navier-Stokes equations, subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation. Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids. Using the trajectory approach, the authors prove the existence of the trajectory attractor for both systems.
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Dedicated to Professor Roger Temam on the Occasion of his 70th Birthday
Project supported by the Italian MIUR-PRIN Research Project 2008 “Transizioni di fase, isteresi e scale multiple”.
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Gal, C.G., Grasselli, M. Trajectory attractors for binary fluid mixtures in 3D. Chin. Ann. Math. Ser. B 31, 655–678 (2010). https://doi.org/10.1007/s11401-010-0603-6
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DOI: https://doi.org/10.1007/s11401-010-0603-6
Keywords
- Navier-Stokes equations
- Allen-Cahn equations
- Cahn-Hilliard equations
- Two-phase fluid flows
- Longtime behavior
- Trajectory attractors