Exact Poincaré constants are derived for annular domains in dimensions 2 to N, with a dimensional correspondence between Stokes and Laplace operators and analysis of thin and wide gap limits.
The Stokes Eigenvalue Problem on balls and annuli in three dimensions: Solutions with Poloidal and Toroidal Fields
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We consider the Stokes eigenvalue problem in open balls and open annuli in R3 with homogeneous Dirichlet boundary conditions. Using the frame of toroidal and poloidal fields we construct the othogonal decomposition of the Stokes eigenvalue problem in problems for toroidal and poloidal eigenfunctions. This provides the proof of the completeness of a system of explicitly calculated Stokes eigenfunctions given by one of the authors in 1999, [14].
fields
math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Derives explicit partial-derivative expressions for gradient and divergence in nD spherical coordinates using the Laplacian and nabla transformations to aid Stokes eigenfunction proofs.
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Exact Poincare Constants in n-dimensional Annuli
Exact Poincaré constants are derived for annular domains in dimensions 2 to N, with a dimensional correspondence between Stokes and Laplace operators and analysis of thin and wide gap limits.
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Explicit formulas for gradients and the divergence in n-dimensional spherical coordinates
Derives explicit partial-derivative expressions for gradient and divergence in nD spherical coordinates using the Laplacian and nabla transformations to aid Stokes eigenfunction proofs.