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Existence of global weak solutions for a phase–field model of a vesicle moving into a viscous incompressible fluid |
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| Authors: | Yuning Liu Takéo Takahashi |
| Institution: | 1. Faculty of Mathematics, University of Regensburg, , 93053 Regensburg, Germany;2. Inria, , 54600 Villers‐lès‐Nancy, France;3. IECN, UMR 7502, Université de Lorraine, , 54506 Vandoeuvre‐lès‐Nancy, France;4. CNRS, IECN, UMR 7502, , 54506 Vandoeuvre‐lès‐Nancy, France |
| Abstract: | 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. Our main result states the existence of weak solutions for the corresponding system. The proof is based on compactness/monotonicity arguments. Copyright © 2013 John Wiley & Sons, Ltd. |
| Keywords: | fluid vesicle interaction vesicle membrane Navier– Stokes phase– field local incompressibility |