Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two
Chen‐Chih Lai, Fanghua Lin, Changyou Wang, Juncheng Wei, Yifu Zhou
Abstract
Abstract We consider the initial boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain Ω ⊂ ℝ 2 . Given any k distinct points in the domain, we develop a new inner‐outer gluing method to construct solutions that blow up exactly at those k points as t goes to a finite time T . Moreover, we obtain a precise description of the blowup. © 2021 Wiley Periodicals LLC.
Topics & Concepts
Liquid crystalBounded functionDomain (mathematical analysis)MathematicsDimension (graph theory)Flow (mathematics)Boundary value problemBoundary (topology)Mathematical analysisGeometryPure mathematicsCondensed matter physicsPhysicsNavier-Stokes equation solutionsGeometric Analysis and Curvature FlowsNonlinear Partial Differential Equations