Pullback attractors of the two-dimensional non-autonomous simplified Ericksen–Leslie system for nematic liquid crystal flows

Abstract

This paper is concerned with the long-time behaviour of the two-dimensional non-autonomous simplified EricksenLeslie system for nematic liquid crystal flows introduced in Lin and Liu (Commun Pure Appl Math, 48:501-537, 1995) with a non-autonomous forcing bulk term and order parameter field boundary conditions. In this paper, we prove the existence of pullback attractors and estimate the upper bound of its fractal dimension under some suitable assumptions.Mathematics Subject Classification. 35B41 · 37L30.