On the flat strong discontinuities in incompressible polymeric liquids

Abstract

We studied the discontinuous stationary solutions for the rheological mesoscopic modified model of Pokrovskii-Vinogradov, which describes the dynamics of liquid polymers. The Rankine-Hugoniot conditions for the model were introduced. We justified the existence of stationary solutions with flat surface of strong discontinuity for the case of constant velocity direction across the discontinuity and for the case with change of direction (rotating discontinuity). The stability of such solutions was also considered. For linearized equations of the model we posed the eigenvalue problem for partial solutions with unlimited grow in time. It was shown that such solutions exists in anisotropic case wich means the stationary solutions with flat discontinuity are unstable within the given model.