| Abstract: |
| The molecules of nematic liquid crystal flow as in a liquid phase; however, they have an orientation order. The orientation order is described by the symmetric, traceless matrix Q. Beris and Edwards proposed a Q-tensor model, the coupled system of the Navier-Stokes equations and a parabolic-type equation describing the evolution of the order parameter Q, to represent nematic liquid crystal flows.
The aim of this talk is to prove the unique existence of the global-in-time solution for small initial data in the maximal regularity class for the Q-tensor model in the half-space $\mathbb R^N_+$, $N \ge 2$. In this talk, we especially discuss the weighted estimates of solutions for the linearized problem to control the higher-order terms of the solutions. This talk is based on joint work with Prof. Yoshihiro Shibata (Waseda University) and Dr. Daniele Barbera (Politecnico di Torino). |
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