References

ON THE POWER OF STOKES OPERATOR


[1] P. Moon and D. E. Spencer, Field Theory Handbook, Springer-Verlag, 1961.

[2] P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, 1953.

[3] R. P. Eisenhart, Separable systems of Stackel, Annals of Mathematics 35(2) (1934), 284-305.
DOI: https://doi.org/10.2307/1968433

[4] P. Moon and D. E. Spencer, Separability conditions for the Laplace and Helmholtz equations, Journal of the Franklin Institute 253(6) (1952), 585-600.
DOI: https://doi.org/10.1016/0016-0032(52)90682-0

[5] P. Moon and D. E. Spencer, Separability in a class of coordinate systems, Journal of the Franklin Institute 254(3) (1952), 227-242.
DOI: https://doi.org/10.1016/0016-0032(52)90460-2

[6] P. Moon and D. E. Spencer, Some coordinate systems associated with elliptic functions, Journal of the Franklin Institute 255(6) (1953), 531-543.
DOI: https://doi.org/10.1016/0016-0032(53)90302-0

[7] P. Moon and D. E. Spencer, Theorems on separability in Riemannian n-space, Proceedings of the American Mathematical Society 3(4) (1952), 635-642.
DOI: https://doi.org/10.1090/S0002-9939-1952-0049439-7

[8] P. Moon and D. E. Spencer, Recent investigations of the separation of Laplace’s equation, Proceedings of the American Mathematical Society 4(2) (1953), 302-307.
DOI: https://doi.org/10.1090/S0002-9939-1953-0053335-X

[9] E. Almansi, Sull’integrazione dell’equazione differenziale Annali di Matematica Pura ed Applicata 2(1) (1899), 1-51.
DOI: https://doi.org/10.1007/BF02419286

[10] J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.

[11] E. Protopapas, On the solution of irrotational Stokes flow in rotational system of coordinates, Submitted for publication.

[12] G. Dassios, M. Hadjinicolaou and A. C. Payatakes, Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates, Quarterly of Applied Mathematics 52(1) (1994), 157-191.
DOI: https://doi.org/10.1090/qam/1262325

[13] M. Hadjinicolaou and E. Protopapas, On the R-semiseparation of the Stokes bi-stream operator in inverted prolate spheroidal geometry, Mathematical Methods in the Applied Sciences 37(2) (2014), 207-211.
DOI: https://doi.org/10.1002/mma.2841

[14] M. Hadjinicolaou and E. Protopapas, Spectral decomposition of the Stokes flow operators in the inverted prolate spheroidal coordinates, IMA Journal of Applied Mathematics 80(5) (2015), 1475-1491.
DOI: https://doi.org/10.1093/imamat/hxv003

[15] M. Hadjinicolaou and E. Protopapas, Eigenfunction expansions for the Stokes flow operators in the inverted oblate coordinate system, Mathematical Problems in Engineering (2016); Article ID 9049131.
DOI: http://dx.doi.org/10.1155/2016/9049131

[16] S. Deo and A. Tiwari, On the solution of a partial differential equation representing irrotational flow in bispherical polar coordinates, Applied Mathematics and Computation 205(1) (2008), 475-477.
DOI: https://doi.org/10.1016/j.amc.2008.08.023

[17] M. Hadjinicolaou and E. Protopapas, Necessary and sufficient conditions for the separability and the R-separability of the irrotational Stokes equation, Submitted for publication.

[18] A. Charalambopoulos and G. Dassios, Complete decomposition of axisymmetric Stokes flow, International Journal of Engineering Science 40(10) (2002), 1099-1111.
DOI: https://doi.org/10.1016/S0020-7225(02)00004-6

[19] G. Dassios and P. Vafeas, On the spheroidal semiseparation for Stokes flow (2008); Article ID 135289.
DOI: https://doi.org/10.1155/2008/135289

[20] N. N. Lebedev, Special Functions and their Applications, Dover Publications, 1972.