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arXiv · 1505.04127

Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model

Blanca Climent-Ezquerra·Francisco Guillén-González
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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.

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Blanca Climent-Ezquerra, Francisco Guillén-González. 2015-05-15. Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model. https://arxiv.org/abs/1505.04127

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