Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

On derivation of compressible fluid systems on an evolving surface


Author: Hajime Koba
Journal: Quart. Appl. Math.
MSC (2010): Primary 37E35, 49S05, 37D35
DOI: https://doi.org/10.1090/qam/1491
Published electronically: October 13, 2017
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Abstract: We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our compressible fluid systems on the evolving surface. Applying the first law of thermodynamics and the Gibbs equation, we investigate the internal energy, enthalpy, entropy, and free energy of the fluid on the evolving surface. We also study conservative forms and conservation laws of our compressible fluid systems on the evolving surface. Moreover, we derive the generalized heat and diffusion systems on an evolving surface from an energetic point of view. This paper gives a mathematical validity of the surface stress tensor determined by the Boussinesq-Scriven law. Using a flow map on an evolving surface and applying the Riemannian metric induced by the flow map are key ideas to analyze fluid flow on the evolving 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

DOI: https://doi.org/10.1090/qam/1491
Received by editor(s): July 19, 2017
Published electronically: October 13, 2017
Additional Notes: This work was partly supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP25887048 and JP15K17580.
Article copyright: © Copyright 2017 Brown University

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