Joint USYD-UNSW Seminar on Stochastic PDEs: Zhewen Feng (UQ) -- Existence and convergence of the Beris-Edwards system

Zoom link: https://unsw.zoom.us/j/87938114945?from=addon Passcode 859718 

The Beris-Edwards system provides a comprehensive hydrodynamic framework for modeling
the flows of nematic liquid crystals.  In this talk, we investigate this system
utilizing the general Landau-de Gennes energy density that satisfies the coercivity
condition for non-zero elastic constants.  We will present two primary mathematical
results: 

(1) The construction and existence of a unique strong solution for the uniaxial
Beris-Edwards system up to a maximal existence time.  (2) The smooth convergence of
strong solutions for biaxial Q-tensors to the uniaxial solution, as the rescaled
dimensionless parameter approaches zero.  

A major focus of the presentation will be a novel rotation technique developed to
overcome the mathematical difficulties associated with the bulk energy density terms.
By using a smooth rotation matrix to transform the Q-tensors into a block-diagonal form
and applying Gagliardo-Nirenberg interpolation, we establish the uniform a-priori energy
estimates crucial for those two results.