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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Dynamic theory for incompressible Smectic-A liquid crystals: Existence and regularity

Pages: 591 - 608, Volume 6, Issue 3, July 2000      doi:10.3934/dcds.2000.6.591

 
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Chun Liu - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: We study a system that was proposed in [3] in order to model the dynamic of Smectic-A liquid crystals. We establish the energy dissipative relation of the system and prove the existence of global weak solutions. A higher order energy estimate is also established for the existence of the classical solutions and the regularity of the weak solutions. Some regularity and stability results are also discussed in this paper.

Keywords:  Smectic-A liquid crystals, Navier-Stokes equations.
Mathematics Subject Classification:  Primary: 35Q30, 35Q72, 35K22.

Received: September 1999;      Revised: December 1999;      Published: April 2000.