Geodesic
The eigenfunctions of curl, gradient of divergence and Stokes operators. Applications
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2013), pp. 131-146

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We consider the spectral problems for curl, gradient of divergence and Stokes operators. The eigenvalues are defined by zeroes of half-integer order Bessel functions and derivatives thereof. The eigenfunctions are given in an explicit form by half-integer order Bessel functions and spherical harmonics. Their applications are described. The completeness of eigenfunctions of curl operator in $\mathbf{L}_{2}(B)$ is proved.
Keywords: curl, Stokes operator, eigenvalues and eigenfunctions of operators, Fourier series.
Mots-clés : gradient of divergence 
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     author = {R. S. Saks},
     title = {The eigenfunctions of curl, gradient of divergence and {Stokes} operators. {Applications}},
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R. S. Saks. The eigenfunctions of curl, gradient of divergence and Stokes operators. Applications. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2013), pp. 131-146. http://geodesic.mathdoc.fr/item/VSGTU_2013_2_a15/