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Publication 19-CNA-015

Anisotropic Micropolar Fluids Subject To A Uniform Microtorque: The Unstable Case

Antoine Remond-Tiedrez
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
aremondt@andrew.cmu.edu

Ian Tice
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
ian.tice@andrew.cmu.edu

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.

Get the paper in its entirety as  19-CNA-015.pdf

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