The Beris-Edward is a hydrodynamic system modeling nematic liquid crystals in the setting of Q-tensor order parameter. Mathematically speaking it is the incompressible Navier-Stokes equations coupled with a Q tensor equation of parabolic type.
We first consider the simplified Beris-Edward system that corresponds to the co-rotational case, and study the eigenvalue preservation property for the initial Q-tensor order parameter in 3D. We work in both the whole space and bounded domain cases, and provide two different proofs. Then we show that for the general system that relates to the non-corotational case, this property is not valid.
Xiang Xu holds his Ph.D. from Pennsylvania State University in 2011. He is assistant professor in Old Dominion University. His research interests are partial differential equations and fluid mechanics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai