(157d) The Weighted Ellipsoidal Metric Space (WEMS) Theorem and Stokes Flow Past an Ellipsoid in a Polynomial Ambient Field

In 1987, Kim and Arunachalam published the general solution for Stokes flow past an ellipsoid immersed in a polynomial ambient velocity field thereby extending the classical results of Oberbeck (translational motions), Edwardes (rotational motions) and Jeffery (linear ambient field). The description of the general solution was limited to the velocity and pressure fields and did not include an analysis of the tractions on the surface of the ellipsoid. The recent (2015) proof that the double layer operator is self-adjoint in a weighted metric space (the weight function w(x) at a point x on the ellipsoid surface is the distance from the center of the ellipsoid to the tangent plane for x) will be used to prove that the tractions on an ellipsoid immersed in the n-th order polynomial ambient field are w(x) times a polynomial of the same degree.