Local and global existence for the Ericksen-Leslie problem in unbounded domains
arXiv:2401.08193 · doi:10.1016/j.jmaa.2024.128677
Abstract
The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of a fixed constant vector. We prove, through a combination of energy method with dispersive a priori estimates, a local existence and a global existence for small initial data by a contraction argument asking low regularity assumptions on the initial condition.
38 pages