WELL-POSEDNESS OF A FULLY-COUPLED NAVIER-STOKES/Q-TENSOR SYSTEM WITH INHOMOGENEOUS BOUNDARY DATA
主 题: WELL-POSEDNESS OF A FULLY-COUPLED NAVIER-STOKES/Q-TENSOR SYSTEM WITH INHOMOGENEOUS BOUNDARY DATA
报告人: Dr. Yuning Liu (University of Regensburg)
时 间: 2014-01-08 10:30-11:30
地 点: 理科一号楼1418（主持人：章志飞）
We consider the wellposedness of the Beris–Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system consists of the Navier-Stokes equations coupled with an evolution equation for the Q-tensor. The solutions possess higher regularity in time of order one compared to the class of weak solutions with finite energy. This regularity is enough to obtain Lipschitz continuity of the non-linear terms in the corresponding function spaces. Therefore the well-posedness is shown with the aid of the contraction mapping principle using that the linearized system is an isomorphism between the associated function spaces.