Journal of Mathematical Sciences: Advances and Applications
POWER OF STOKES OPERATORAuthor's: Eleftherios Protopapas
Pages: [1] - [10]
Received Date: June 26, 2020; Revised July 2, 2020
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122139
Stokes operators, 
are well known partial differential operators
of elliptic type, which are often used in Applied Mathematics. Stokes
equation 
describes the irrotational, axisymmetric
creeping flow and Stokes bi-stream equation denotes the rotational one, where 
Necessary and sufficient conditions for the
separability and the R-separability of the equation have been proved recently. Moreover, the
0-eigenspace and the generalized 0-eigenspace of the operator
have been derived in several coordinate
systems. Specifically, the spherical coordinate system is employed in
many problems taking into account that in many engineering
applications, the solutions in spherical geometry seem to be adequate
for solving a problem. In the present manuscript, it is shown that
equation 
admits a solution of the form 
where 
are solutions of Stokes equation and r
is the radial spherical variable. Additionally, we obtain the kernel
of the 
power of the Stokes operator, 
in the spherical geometry for every 
Stokes operator, eigenfunctions, spherical system of coordinates, Gegenbauer functions.
