Abstract
We derive the biorthogonality condition for axisymmetric Stokes flow in a region between two concentric spheres. This biorthogonality condition is a property satisfied by the eigenfunctions and adjoint eigenfunctions, which is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding creeping flow problem.
Highlights
The eigenfunction expansion method has been used extensively for solving problems of Stokes flow
The method leads to the development of a set of eigenfunctions, adjoint eigenfunctions, biorthogonality conditions and an algorithm for the computation of the eigenfunction expansions
Similar biorthogonal eigenfunction expansions and biorthogonality conditions are required for the axisymmetric Stokes flow problems in a wedge shaped trench studied by Liu and Joseph [7], the axisymmetric Stokes flow in a cone studied by Liu and Joseph [8] and for the problem of Stokes flow in a trench between concentric cylinders studied by Yoo and Joseph [11]
Summary
The eigenfunction expansion method has been used extensively for solving problems of Stokes flow. The method leads to the development of a set of eigenfunctions, adjoint eigenfunctions, biorthogonality conditions and an algorithm for the computation of the eigenfunction expansions. The previous references are just a small sample of problems arising in Stokes flow and elasticity which can be solved in biorthogonal series of eigenfunctions generated by separating variables.
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