Date/Time
Date(s) - 19/01/2024
1:30 pm - 2:30 pm

Location: HH 410

Speaker: Gael Yomgne Diebou (University of Toronto)

Title: Asymptotics and stability of global solutions to liquid crystal flows in three dimensions.

Abstract: In this talk, I will discuss the question of blow up of a priori global solutions to nematic liquid crystal flow. The latter is a hydrodynamic system modelling the flow of liquid crystal materials and it couples the nonhomogeneous Navier-Stokes equations with the transported harmonic maps heat flow into the 2-sphere.
The main result I plan to present could be summarized as follows. An a priori global solution arising from large initial data in VMO (vanishing mean oscillations) becomes small at large times. This smallness at infinity implies a stability result: A small perturbation of the initial data (u_0,d_0) in the topology of BMO^{-1}\times BMO gives rise to another solution (v,\widetilde{d}) in the same space, at a small distance (independent on time) of the reference solution. I will emphasize on the crucial role of the geometric condition enabling us to obtain a cancellation property, which is a key ingredient in establishing the non-blow-up result.