Existence of global weak solutions for a phase–field model of a vesicle moving into a viscous incompressible fluid. (9th July 2013)

• Record Type: Journal Article
• Authors: Liu, Yuning; Takahashi, Takéo
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 10(2014:Jul. 15)
• Page Start: 1507
• Page End: 1526
• Publication Date: 2013-07-09
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2912
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2912-abs-0001"> <title>Abstract</title> <p>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 &amp; Sons, Ltd.</p> </abstract>