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The Quarterly Journal of Mechanics and Applied Mathematics 1992 45(1):47-56; doi:10.1093/qjmam/45.1.47
© 1992 by Oxford University Press
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LAMB'S SOLUTION OF STOKES'S EQUATIONS: A SPHERE THEOREM

D. PALANIAPPAN, S. D. NIGAM, T. AMARANATH and R. USHA

( School of Mathematics and Computer/Information Sciences, University of Hyderabad Hyderabad 500 134, India
Department of Mathematics, Anna University Madras 600 025, India )

The velocity and pressure in Stokes flow are written in terms of two functions A and B, where A is biharmonic and B is harmonic. Lamb's (1) general solution of Stokes's equations and Oseen's (2) solution due to a Stokeslet in the presence of a no-slip spherical boundary have the same structure as our representation. Ranger's (3) representation follows as a special case of our result.

A sphere theorem for non-axisymmetric flow outside or inside a sphere is stated and proved. Collins's theorem (4) for axisymmetric flow follows as a special case of our theorem. A few illustrative examples are given and in each case the drag and torque on the sphere are calculated.


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