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Global well-posedness and standing wave solutions for a class of nematic liquid crystal system

Feixiang Li
Kaimin Teng ; Department of Mathematics, Taiyuan University of Technology, Taiyuan, China

Puni tekst: engleski pdf 160 Kb

str. 257-276

preuzimanja: 56



This paper is devoted to studying the Cauchy problem and standing wave for a class of nematic liquid crystal system. This system appears in the recent studies of the propagation of a laser beam in a nematic liquid crystal. The above system couples a Schr\"{o}dinger evolution equation to a nonlinear elliptic equation which describes the response of the director angle to the laser beam electric field. The global well-posedness will be established through using Banach fixed point theorem and continuity argument. Secondly, the existence of standing wave solution is established through using the constrained minimization approach.

Ključne riječi

Ground state solutions; well-posedness; Nehari manifold; minimization

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