Linear stability of the rest state of viscoelastic liquid in the circular pipe under the effect of magnetic field

We have studied the eigenvalue problem for the rest state of the viscoelastic liquid in an infinite cylinder with a uniform magnetic field directed along the centerline of the cylinder. It was shown for axisymmetric disturbances that the eigenspectrum has negative real parts regardless of the values of the parameters presented in the problem. For the simplified case of a perfectly conducting liquid, we obtained the eigenfunctions of the problem, while in the general case, we justified the stability of the state by the energy estimates.