Large time behavior for MHD micropolar fluids in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>

Cruz, F.W.; Perusato, Cilon; Rojas-Medar, Marko Antonio; Zingano, Paulo R.

doi:10.1016/j.jde.2021.12.013

Cited by 14 publications

(2 citation statements)

References 31 publications

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“…When the initial data are also in L 1 , the corresponding results were obtained in [11] by combining the monotonicity approach of [22,27] with the Fourier Splitting technique introduced by M. Schonbek in [36,37]. Using the decay character theory, C. Niche and C. Perusato [32] derived lower bounds for (u, w)(•, t) L 2 .…”

Section: Introductionmentioning

confidence: 99%

On the spontaneous synchronization between micro-rotation and vorticity in micropolar flows

Guterres¹,

Wilberclay²,

Perusato³

et al. 2022

Preprint

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The spontaneous synchronization between micro-rotation and vorticity in micropolar flows in R n (n = 2, 3) is investigated and used to explain the faster decay by t −1/2 of the angular velocity of the fluid particles' microrotation, as well as establishing its optimality. This synchronization effect remained elusive for sixty years of investigations in micropolar fluid flows and was revealed after important upper and lower bounds for the solutions in Ḣm (R n ) were obtained by the authors, using the monotonicity approach for general dissipative systems introduced in [22]. Several related results of independent interest are also given along the discussion.

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Section: Introductionmentioning

confidence: 99%

On the spontaneous synchronization between micro-rotation and vorticity in micropolar flows

Guterres¹,

Wilberclay²,

Perusato³

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…[3,12] for decay results). Also, we briefly refer to Cruz et al [8] and Kreiss et al [14] for the related fluid equations.…”

Section: Introductionmentioning

confidence: 99%

Decay estimates for a class of non‐Newtonian 3D magneto‐micropolar fluids

Kim

2022

Z Angew Math Mech

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Local Well‐Posedness to the Magneto‐Micropolar Boundary Layer Equations in Gevrey Space

Tan,

Zhang

2024

Math Methods in App Sciences

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We study the boundary layer equations for two‐dimensional magneto‐micropolar boundary layer system and establish the existence and uniqueness of solutions in the Gevrey function space without any structural assumption, with Gevrey index . Inspired by the abstract Cauchy‐Kovalevskaya theorem, our proof is based on a new cancellation mechanism in the system to overcome the difficulties caused by the loss of derivatives. Our results improve the classical local well‐posedness results presented in a previous study, specifically for cases where the initial data are analytic in the ‐variable.

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Large time behavior for MHD micropolar fluids in Rn

Cited by 14 publications

References 31 publications

On the spontaneous synchronization between micro-rotation and vorticity in micropolar flows

On the spontaneous synchronization between micro-rotation and vorticity in micropolar flows

Decay estimates for a class of non‐Newtonian 3D magneto‐micropolar fluids

Local Well‐Posedness to the Magneto‐Micropolar Boundary Layer Equations in Gevrey Space

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