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Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model
- Publication Year :
- 2015
-
Abstract
- In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the membrane, coupled with a Cahn-Hilliard phase-field equation associated to a bending energy plus a penalization term related to the area conservation. This problem has a dissipative in time free-energy which leads, in particular, to prove the existence of global in time weak solutions. We analyze the large-time behavior of the weak solutions. By using a modified Lojasiewicz-Simon's result, we prove the convergence as time goes to infinity of each (whole) trajectory to a single equilibrium. Finally, the convergence of the trajectory of the phase is improved by imposing more regularity on the domain and initial phase.
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1505.04127
- Document Type :
- Working Paper