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

Wenjing Zhao

doi:10.3934/dcds.2018203

Article Contents

2018, Volume 38, Issue 9: 4637-4655. Doi: 10.3934/dcds.2018203

This issue Previous Article Weak-strong uniqueness for the general Ericksen—Leslie system in three dimensions Next Article Lyapunov stability for regular equations and applications to the Liebau phenomenon

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

Wenjing Zhao^,

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

* Corresponding author: Wenjing Zhao
* Corresponding author: Wenjing Zhao

Received: December 2017

Published: September 2018

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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.

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Mathematics Subject Classification: Primary: 35A01, 35B44; Secondary: 76A10.

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References

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