Abstract
We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain.
By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems.
By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed.
We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.
Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung
