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Some properties on the Q-Tensor system


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Author: Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles
Coordinator/Director: López de Silanes Busto, María Cruz
Palacios Latasa, Manuel Pedro
Sanz Sáiz, Gerardo
Amrouche, Chérif
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2014
Published in: Twelfth International Conference Zaragoza-Pau on Mathematics: Jaca (Spain), September 17-19, 2012
ISBN/ISSN: 9788416028351
Document type: Chapter of Book
Abstract: We study the coupled Navier-Stokes and Q-Tensor system (analyzed in cf. [Paicu, M., and Zarnescu, A. Energy dissipation and regularity for a coupled Navier-Stokes and Q-tensor system. Arch. Ration. Mech. Anal. 203 (2012), 45–67] in the whole R3) in a bounded three-dimensional domain for several boundary conditions, rewriting the system in a way that properties as symmetry and null-trace for the tensor Q can be proved. We show some analytical results such as: the existence of global in time weak solution, a maximum principle for the Q-tensor, local in time strong solution (which is global assuming an additional regularity criterion for the velocity in the space-periodic boundary condition case), global in time strong solution imposing dominant viscosity (for the space-periodic or homogeneous Neumann boundary condition cases) and regularity criteria for uniqueness of weak solutions.
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