Anisotropic micropolar fluids subject to a uniform microtorque: the unstable case

2019/10/28 by Antoine Remond-Tiedrez, Ian Tice, Remond-Tiedrez, Antoine +1 · 1 citation
Computer Science · Engineering · Mathematics · #35B35 #35P15 #35Q30 (Secondary) #74A60 #76A05 (Primary) 35M31 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.12942

openalex publication_date 2019/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 L²-level.

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