Existence of global weak solutions for a phase-field model of a vesicle moving into a viscous incompressible fluid

Yuning Liu (1) , Takéo Takahashi (2, 3)

1 UR - Universität Regensburg
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECL - Institut Élie Cartan de Lorraine

We consider in this article a model of vesicle moving into a viscous incompressible fluid. The vesicle is described through a phase-field equation and through a transport equation modeling the local incompressibility of its membrane. The equations for the fluid are the classical Navier--Stokes equations with a force resulting from the presence of the vesicle. The model for the system vesicle--fluid is an approximation of a model obtained by Jamet and Misbah. Our main result states the existence of weak solutions for the corresponding system. The proof is based on compactness/monotonicity arguments

Mots clés: vesicle membrane; fluid vesicle interaction; phase-field; local incompressibility; Navier-Stokes

Domaines: Equations aux dérivées partielles [math.AP]

Yuning Liu, Takéo Takahashi. Existence of global weak solutions for a phase-field model of a vesicle moving into a viscous incompressible fluid. Mathematical Methods in the Applied Sciences, 2014, 37 (10), pp.1507-1526. ⟨10.1002/mma.2912⟩. ⟨hal-00914930⟩