Analysis and PDE Seminar: Instability of an Anisotropic Micropolar Fluid

Friday, October 30, 2020 at 2:00pm to 3:00pm

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Antoine Remond-Tiedrez, University of Wisconsin-Madison

Many aerosols and suspensions, or more broadly fluids containing a non-trivial structure at a microscopic scale, can be described by the theory of micropolar fluids. The resulting equations couple the Navier-Stokes equations which describe the macroscopic motion of the fluid to evolution equations for the angular momentum and the moment of inertia associated with the microcopic structure. In this talk we will discuss the case of viscous incompressible three-dimensional micropolar fluids. We will discuss how, when subject to a fixed torque acting at the microscopic scale, the nonlinear stability of the unique equilibrium of this system depends on the shape of the microstructure.

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