ON GLOBAL BEHAVIOR OF WEAK SOLUTIONS OF COMPRESSIBLE FLOWS OF NEMATIC LIQUID CRYSTALS

doi:10.1016/S0252-9602(15)30011-4

Abstract

Abstract:

In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier--Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ >5/3.

Key words: Liquid crystals, weak solutions, bounded absorbing set, bounded trajectories, attractor

CLC Number:

35Q35

Weiwei WANG. ON GLOBAL BEHAVIOR OF WEAK SOLUTIONS OF COMPRESSIBLE FLOWS OF NEMATIC LIQUID CRYSTALS[J].Acta mathematica scientia,Series B, 2015, 35(3): 650-672.

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