Local well-posedness and blow-up criteria of magneto-viscoelastic flows

Abstract

In this paper, we investigate a hydrodynamic system that models the dynamics of incompressible magneto-viscoelastic flows. First, we prove the local well-posedness of the initial boundary value problem in the periodic domain. Then we establish a blow-up criterion in terms of the temporal integral of the maximum norm of the velocity gradient. Finally, an analog of the Beale-Kato-Majda criterion is derived.