Abstract: We study a linear stability of a resting state for flows of incompressible viscoelastic fluid in a infinite cylindrical channel under the influence of an external uniform magnetic field directed parallel to the cylinder axis(we use a generalized rheological Vinogradov-Pokrovsky model as mathematical model) in a class of axisymmetric variable flows. We establish that for some values of the parameters in the case of an absolute conductivity the magnetic field can substantially lessen the real part of an exponent for perturbations of the radial velocity component, which is the main element of the instability development. For general case we justify the possibility of removing the instability based on the performed calculations.

Cite: Tkachev D.L. , Biberdorf E.A. , Yegitov A.V.
Linear instability of a resting state of the magnetohydrodynamic flows of a polymeric fluid in a cylindrical channel
2026 China-Russia Conference of Mathematics (Nanjing) 19-25 Apr 2026