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arXiv · 1710.00469

Asymptotic behavior of global weak solutions for the micropolar dynamics in $L^{2}(\mathbb{R}^{3})$

Robert Guterres·Juliana Nunes·Cilon Perusato
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Abstract

In this paper the long time behavior of the micropolar fluid equations energy on three dimensional space are studied. We show that $ \| (u,w)(\cdot,t) \|_{{L^{2}(\mathbb{R}^{3})}} \to 0 $ as $t \to \infty$ for Leray-Hopf's global weak solutions in inviscid vortex case. Moreover, when the vortex viscosity are considered, i.e., $\chi >0$, we obtain a (faster) decay for micro-rotational field: $ \| w (\cdot,t) \|_{{L^{2}(\mathbb{R}^{3})}} = o(t^{-1/2})$.

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Robert Guterres, Juliana Nunes, Cilon Perusato. 2017-10-02. Asymptotic behavior of global weak solutions for the micropolar dynamics in $L^{2}(\mathbb{R}^{3})$. https://arxiv.org/abs/1710.00469

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