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Analysis of Micropolar Fluids: Existence of Potential Microflow Solutions, Nearby Global Well-Posedness, and Asymptotic Stability

Analysis of Micropolar Fluids: Existence of Potential Microflow Solutions, Nearby Global... In this paper we concern ourselves with an incompressible, viscous, isotropic, and periodic micropolar fluid. We find that in the absence of forcing and microtorquing there exists an infinite family of well-behaved solutions, which we call potential microflows, in which the fluid velocity vanishes identically, but the angular velocity of the microstructure is conservative and obeys a linear parabolic system. We then prove that nearby each potential microflow, the nonlinear equations of motion are well-posed globally-in-time, and solutions are stable. Finally, we prove that in the absence of force and microtorque, solutions decay exponentially, and in the presence of force and microtorque obeying certain conditions, solutions have quantifiable decay rates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Analysis of Micropolar Fluids: Existence of Potential Microflow Solutions, Nearby Global Well-Posedness, and Asymptotic Stability

Acta Applicandae Mathematicae , Volume 170 (1) – Dec 30, 2020

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References (27)

Publisher
Springer Journals
Copyright
Copyright © Springer Nature B.V. 2020
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-020-00363-5
Publisher site
See Article on Publisher Site

Abstract

In this paper we concern ourselves with an incompressible, viscous, isotropic, and periodic micropolar fluid. We find that in the absence of forcing and microtorquing there exists an infinite family of well-behaved solutions, which we call potential microflows, in which the fluid velocity vanishes identically, but the angular velocity of the microstructure is conservative and obeys a linear parabolic system. We then prove that nearby each potential microflow, the nonlinear equations of motion are well-posed globally-in-time, and solutions are stable. Finally, we prove that in the absence of force and microtorque, solutions decay exponentially, and in the presence of force and microtorque obeying certain conditions, solutions have quantifiable decay rates.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 30, 2020

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