A spectral method for Stokes equations

摘要

We find a spectral method for the solutions to Stokes equations in the spherical domain. We represent the solutions in terms of spherical harmonics and find an algorithm deciding each coefficient of the given degree. Concrete power series expansions using the associated three-dimensional Legendre functions and two-dimensional complex variable functions are derived. Moreover the pressure can be decided from structure theorems for homogeneous solutions.