Anisotropic Micropolar Fluids Subject to a Uniform Microtorque: The Unstable Case

We study a three-dimensional, incompressible, viscous, micropolar fluid with anisotropic microstructure on a periodic domain. Subject to a uniform microtorque, this system admits a unique nontrivial equilibrium. We prove that this equilibrium is nonlinearly unstable. Our proof relies on a nonlinear...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 381; no. 3; pp. 947 - 999
Main Authors Remond-Tiedrez, Antoine, Tice, Ian
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Complex Systems
Control stability
Fluid dynamics
Fluid flow
Incompressible flow
Mathematical and Computational Physics
Mathematical Physics
Micropolar fluids
Norms
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We study a three-dimensional, incompressible, viscous, micropolar fluid with anisotropic microstructure on a periodic domain. Subject to a uniform microtorque, this system admits a unique nontrivial equilibrium. We prove that this equilibrium is nonlinearly unstable. Our proof relies on a nonlinear bootstrap instability argument which uses control of higher-order norms to identify the instability at the L 2 level.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03928-5