The eigenfunctions of curl, gradient of divergence and Stokes operators. Applications

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.