Speaker: Pro.Changyou Wang（Purdue University of USA）

Title: Suitable weak solutions of Beris-Edwards $Q$-tensor system in dimension three

Time: Mon, Jun.24, AM:10:20-11:20

Location: Room 4131, Building No.4, Wushan Campus

Abstract:

        In this talk, we will introduce a hydrodynamic system, involving using the $Q$-tensors introduced by De Gennes, proposed by Beris and Edwards to model the motion of nematic liquid crystal materials. Mathematically it is a system coupling the Navier-Stokes equation and a parabolic-like system of $Q$-tensors. In dimension three, we show the existence of suitable weak solutions of Beris-Edwards system associated with either Landau-De Gennes polynomial type regular bulk potential or Maire-Saupe (or Ball-Majumdar) singular bulk potential, and then prove its partial smoothness asserting that it is smooth away from a closed set of 1 dimension parabolic Hausdorff measure zero. This is joint with Hengrong Du (Purdue) and Xianpeng Hu (City U of HongKong).