Display Abstract

Title Convergence to equilibrium for smectic-A liquid crystals in 3D domains

Name Francisco Guillen-Gonzalez
Country Spain
Email guillen@us.es
Co-Author(s) Blanca Climent-Ezqierra
Submit Time 2014-01-31 13:47:13
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
In this talk, we focus on a smectic-A liquid crystal model in 3D domains, obtaining three main results: the proof of an adequate Lojasiewicz-Simon inequality in a strong framework, the rigorous proof (via a Galerkin approach) of the existence of global in time weak solutions which are strong (and unique) for large times, and the convergence to equilibrium of the whole trajectory as time goes to infinity. Given any regular initial data, the existence of a unique global in time regular solution (bounded up to infinite time) and the convergence to an equilibrium have been previously proved, but under the constraint of large enough viscosity. Now, all results are obtained without imposing large viscosity.