Small Data Global Regularity for the 3-D Ericksen--Leslie Hyperbolic Liquid Crystal Model without Kinematic Transport
Jiaxi Huang, Ning Jiang, Yi-Long Luo, Lifeng Zhao
Abstract
In this article, we consider the Ericksen-Leslie's hyperbolic system for incompressible liquid crystal model without kinematic transport in three spatial dimensions, which is a nonlinear coupling of incompressible Navier-Stokes equations with wave map to $\mathbb{S}^2$. Global regularity for small and smooth initial data near the equilibrium is proved. The proof relies on the idea of space-time resonance.
Topics & Concepts
KinematicsMathematicsSmall dataMathematical analysisNonlinear systemCoupling (piping)Kinematic waveLiquid crystalGeometryClassical mechanicsHyperbolic equilibrium pointHyperbolic partial differential equationWork (physics)Hyperbolic manifoldHyperbolic functionCrystal (programming language)Wave propagationTraveling waveInitial value problemNavier-Stokes equation solutionsStability and Controllability of Differential EquationsAdvanced Mathematical Physics Problems