# American Institute of Mathematical Sciences

September  2018, 38(9): 4637-4655. doi: 10.3934/dcds.2018203

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

 Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China

* Corresponding author: Wenjing Zhao

Received  December 2017 Published  June 2018

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.

Citation: Wenjing Zhao. Local well-posedness and blow-up criteria of magneto-viscoelastic flows. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4637-4655. doi: 10.3934/dcds.2018203
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