# American Institute of Mathematical Sciences

July  2000, 6(3): 591-608. doi: 10.3934/dcds.2000.6.591

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

 1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Received  September 1999 Revised  December 1999 Published  April 2000

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.
Citation: Chun Liu. Dynamic theory for incompressible Smectic-A liquid crystals: Existence and regularity. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 591-608. doi: 10.3934/dcds.2000.6.591
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