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

Chun Liu

doi:10.3934/dcds.2000.6.591

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2000, Volume 6, Issue 3: 591-608. Doi: 10.3934/dcds.2000.6.591

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

Chun Liu^1,

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

Received: September 1999

Revised: December 1999

Published: July 2000

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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.

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