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Guterres, Robert; Nunes, Juliana; Perusato, Cilon

doi:10.1016/j.nonrwa.2018.08.002

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…for every m ≥ 0, see e.g. [15,16]. The extra factor t 1/2 in (1.5b) as compared to (1.5a) seems to have been first obtained in the incompressible case in [14,23] (for compressible flows, see [20]), as a consequence of the damping term in the equation (1.1c).…”

Section: Introductionmentioning

confidence: 88%

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Vorticity and Micro-Rotation in Micropolar Flows

Zingano¹,

Niche²,

Perusato³

et al. 2022

Preprint

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In this work the close relation between vorticity and micro-rotation in micropolar flows in Rn (n = 2 or 3) is identified and used to explain the faster decay by t^(-1/2) of the angular velocity of the micro-rotation of fluid particles, as well as establishing its optimality. For this purpose important upper and lower bounds for Leray solutions in homogeneous Sobolev spaces are derived, using the monotonicity approach recently introduced by the authors for dissipative systems in general. Several related results of interest are also given along the discussion.

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Section: Introductionmentioning

confidence: 88%

“…[24]). Since (2.4) is also valid for n = 2, it follows that [14,16,23]), this condition is satisfied for suitable t * * , which depends on how fast z(•, t) L 2 (R 2 ) becomes small for t 1.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Vorticity and Micro-Rotation in Micropolar Flows

Zingano¹,

Niche²,

Perusato³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…[38]). Since (2.4) is also valid for n = 2, it follows that [23]), this condition is satisfied for suitable t * * , which depends on how fast z(•, t) L 2 (R 2 ) becomes small for t 1.…”

Section: Mathematical Preliminariesmentioning

confidence: 94%

“…for every m ≥ 0, see [21,23,32]. The extra factor t 1/2 in (1.5b) as compared to (1.5a) seems to have been first obtained in the incompressible case in [21,23] (for compressible flows, see [30]), as a consequence of the damping term in the equation (1.1c).…”

Section: Introductionmentioning

confidence: 91%

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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Stability and large time decay for the three-dimensional magneto-micropolar equations with mixed partial viscosity

2023

Z. Angew. Math. Phys.

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On the large time decay of global solutions for the micropolar dynamics inL2(Rn)

Cited by 9 publications

References 21 publications

Vorticity and Micro-Rotation in Micropolar Flows

Vorticity and Micro-Rotation in Micropolar Flows

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

Stability and large time decay for the three-dimensional magneto-micropolar equations with mixed partial viscosity

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