Decay rates for the magneto-micropolar system in $$\varvec{L^2(}\pmb {\mathbb {R}}^{\varvec{n)}}$$ |
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Authors: | Robert H Guterres Juliana R Nunes Cilon F Perusato |
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Institution: | 1.Department of Pure and Applied Mathematics,Universidade Federal do Rio Grande do Sul,Porto Alegre,Brazil |
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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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