Weak solutions for an initial–boundary Q-tensor problem related to liquid crystals. (January 2015) - Guillén-González, Francisco; Rodríguez-Bellido, María Ángeles
Abstract: The coupled Navier–Stokes and Q-tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet boundary conditions for the velocity u and either nonhomogeneous Dirichlet or homogeneous Neumann boundary conditions for the tensor Q . The corresponding initial-value problem in the whole space R 3 was analyzed in Paicu and Zarnescu (2012). In this paper, three main results concerning weak solutions will be proved: the existence of global in time weak solutions (bounded up to infinite time), a uniqueness criteria and a maximum principle for Q . Moreover, we identify how to modify the system to deduce symmetry and traceless for Q, for any weak solution. The presence of a stretching term in the Q -system plays a crucial role in all the analysis.