The well-posedness of incompressible magneto-viscoelastic hydrodynamics

Hui Liu; Hui Liu

doi:10.3934/math.2026358

AIMS Mathematics

2026, Volume 11, Issue 3: 8692-8715. doi: 10.3934/math.2026358

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Research article

The well-posedness of incompressible magneto-viscoelastic hydrodynamics

Hui Liu ^,

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

Received: 26 February 2026 Revised: 23 March 2026 Accepted: 27 March 2026 Published: 31 March 2026
MSC : 35A01, 35B45, 35B65, 35Q35, 76D03

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.
- magneto-viscoelasticity,
- Landau-Lifshitz-Gilbert equation,
- complex fluids,
- global well-posedness
Citation: Hui Liu. The well-posedness of incompressible magneto-viscoelastic hydrodynamics[J]. AIMS Mathematics, 2026, 11(3): 8692-8715. doi: 10.3934/math.2026358

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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.

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