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Research Article | Open Access

The well-posedness of incompressible magneto-viscoelastic hydrodynamics

School of Finance and Mathematics, Huainan Normal University, Huainan 232038, China
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Abstract

In this paper, we focused on the evolutionary model for magneto-viscoelasticity. First, we proved the local-in-time existence of classical solutions with finite initial energy for the system by the energy method. Furthermore, the global well-posedness of the magneto-viscoelastic system with small initial data was established in the absence of an external magnetic field.

Keywords

magneto-viscoelasticityLandau-Lifshitz-Gilbert equationcomplex fluidsglobal well-posedness
CLC number: 35A01, 35B45, 35B65, 35Q35, 76D03

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AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 8692-8715
DOI: 10.3934/math.2026358

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Cite this article:
Liu H. The well-posedness of incompressible magneto-viscoelastic hydrodynamics. AIMS Mathematics, 2026, 11(3): 8692-8715. https://doi.org/10.3934/math.2026358

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Received: 26 February 2026
Revised: 23 March 2026
Accepted: 27 March 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)