Abstract
In this paper, the large time decay of the magneto-micropolar fluid equations on \(\mathbb {R}^n\) (\( n=2,3\)) is studied. We show, for Leray global solutions, that \( \Vert ({\varvec{u}},{\varvec{w}},{\varvec{b}})(\cdot ,t) \Vert _{{L^2(\mathbb {R}^n)}} \rightarrow 0 \) as \(t \rightarrow \infty \) with arbitrary initial data in \( L^2(\mathbb {R}^n)\). When the vortex viscosity is present, we obtain a (faster) decay for the micro-rotational field: \( \Vert {\varvec{w}}(\cdot ,t) \Vert _{{L^2(\mathbb {R}^n)}} = o(t^{-1/2})\). Some related results are also included.
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Guterres, R.H., Nunes, J.R. & Perusato, C.F. Decay rates for the magneto-micropolar system in \(\varvec{L^2(}\pmb {\mathbb {R}}^{\varvec{n)}}\). Arch. Math. 111, 431–442 (2018). https://doi.org/10.1007/s00013-018-1186-9
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DOI: https://doi.org/10.1007/s00013-018-1186-9