Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model
Abstract
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in 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.
Keywords
Cite
@article{arxiv.1505.04127,
title = {Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model},
author = {Blanca Climent-Ezquerra and Francisco Guillén-González},
journal= {arXiv preprint arXiv:1505.04127},
year = {2017}
}