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In this paper, we first prove the local-in-time existence of the evolutionarymodel for magnetoelasticity with finite initial energy by employing thenonlinear iterative approach given in \cite{Jiang-Luo-2019-SIAM} to deal withthe geometric constraint $M \in \mathbb{S}^{d-1}$ in theLandau-Lifshitz-Gilbert (LLG) equation. Inspired by\cite{Lin-Liu-Zhang-CPAM2005, Lin-Zhang-2008-CPAM}, we reformulate theevolutionary model for magnetoelasticity with vanishing external magnetic field$H_{ext}$, so that a further dissipative term will be sought from the elasticstress. We thereby justify the global well-posedness to the evolutionary modelfor magnetoelasticity with zero external magnetic field under small size ofinitial data.

Global classical solutions to an evolutionary model for magnetoelasticity