Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Energetic variational approaches for incompressible fluid systems on an evolving surface

Authors: Hajime Koba, Chun Liu and Yoshikazu Giga
Journal: Quart. Appl. Math. 75 (2017), 359-389
MSC (2010): Primary 37E35, 97M50, 49S05, 49Q20, 35A15
DOI: https://doi.org/10.1090/qam/1452
Published electronically: August 25, 2016
Erratum: Quart. Appl. Math. 76 (2018), 147-152.
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper considers the equations governing incompressible fluid-flow on an evolving surface. We employ an energetic variational approach to derive the dynamical system for the motion of incompressible fluid on such an evolving surface. The focus is to understand the coupling of an incompressible fluid-flow and the evolution of a moving surface, involving both the curvature and the motion of the surface.

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Additional Information

Hajime Koba
Affiliation: Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho, Toyonaka, Osaka, 560-8531, Japan
Email: iti@sigmath.es.osaka-u.ac.jp

Chun Liu
Affiliation: Department of Mathematics, 107A McAllister Building, Pennsylvania State University, University Park, Pennsylvania 16802
Email: liuc@psu.edu

Yoshikazu Giga
Affiliation: Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan
Email: labgiga@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/qam/1452
Received by editor(s): April 13, 2016
Published electronically: August 25, 2016
Additional Notes: The work of the first author was partly supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP25887048 and JP15K17580.
The work of the second author was partially supported by National Science Foundation grants DMS-1412005 and DMS-1216938
The work of the third author was partly supported by JSPS through the grants Kiban S number 26220702 and Kiban B number 16H03948
Article copyright: © Copyright 2016 Brown University

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