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Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids

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Abstract

We characterize the \(L^2\) decay rate of solutions to the 3D magneto-micropolar system in terms of the decay character of the initial datum. Due to a linear damping term, the microrotational field has a faster decay rate. We also address the asymptotic behaviour of solutions by comparing them to solutions to the linear part. As a result of the linear damping, the difference between the microrotational field and its linear part also decays faster. As part of the proofs of these results, we prove estimates for the derivatives of solutions which might be of independent interest.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, CEP 21941-909, Brazil

    César J. Niche

  2. Departamento de Matemática, Universidade Federal de Pernambuco, Recife, PE, CEP 50740-560, Brazil

    Cilon F. Perusato

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  1. César J. Niche
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Correspondence to César J. Niche.

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C.J. Niche acknowledges support from Bolsa PQ CNPq - 308279/2018-2 and PROEX - CAPES. C.J. Niche and C.F. Perusato acknowledge support from PRONEX-FAPERJ “Equações Diferenciais Parciais Não Lineares e Aplicações”. C. F. Perusato was partially supported by CAPES–PRINT - 88881.311964/2018–01 and Propesq-UFPE - 08-2019 (Qualis A). He is also grateful for the warm hospitality during his visit at the Universidade Federal do Rio de Janeiro, where this work was started.

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Niche, C.J., Perusato, C.F. Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids. Z. Angew. Math. Phys. 73, 48 (2022). https://doi.org/10.1007/s00033-022-01683-2

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