Oberseminar Mathematik in den Naturwissenschaften: Tao Huang, Weak compactness of simplified nematic liquid flows in 2D

Abstract:

For any bounded smooth domain in dimension two, we will establish the weak compactness property of solutions to the simplified Ericksen-Leslie system for both uniaxial and biaxial nematics, and the convergence of weak solutions of the Ginzburg-Landau type nematic liquid crystal flow to a weak solution of the simplified Ericksen-Leslie system as the parameter tends to zero. This is based on the compensated compactness property of the Ericksen stress tensor, which is obtained by the L p -estimate of the Hopf differential for the Ericksen-Leslie system and the Pohozaev type argument for the Ginzburg-Landau type nematic liquid crystal flow.