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

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.