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Meromorphic non-integrability of a steady Stokes flow inside a sphere

Published online by Cambridge University Press:  15 November 2012

TAKAHIRO NISHIYAMA
TAKAHIRO NISHIYAMA*
Affiliation:
Department of Applied Science, Yamaguchi University, Ube 755-8611, Japan (email: t-nishi@yamaguchi-u.ac.jp)
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Abstract

The non-existence of a real meromorphic first integral for a spherically confined steady Stokes flow of Bajer and Moffatt is proved on the basis of Ziglin’s theory and the differential Galois theory. In the proof, the differential Galois group of a second-order Fuchsian-type differential equation associated with normal variations along a particular streamline is shown to be a special linear group according to Kovacic’s algorithm. A set of special values of a parameter contained in the Fuchsian-type equation is studied by using the theory of elliptic curves. For this set, a computer algebra system is used in part of Kovacic’s algorithm.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 2 , April 2014 , pp. 616 - 627
Copyright
©2012 Cambridge University Press 

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