Regularity criteria for a simplified Ericksen-Leslie system modeling the flow of liquid crystals

Jishan Fan; Tohru Ozawa

doi:10.3934/dcds.2009.25.859

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2009, Volume 25, Issue 3: 859-867. Doi: 10.3934/dcds.2009.25.859

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Regularity criteria for a simplified Ericksen-Leslie system modeling the flow of liquid crystals

Jishan Fan^1, and
Tohru Ozawa^2,

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037
2.
Department of Applied Physics, Waseda University, Tokyo, 169-8555

Received: June 2008

Revised: April 2009

Published: September 2009

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Abstract

We consider the hydrodynamic theory of liquid crystals. We prove some regularity criteria for a simplified Ericksen-Leslie system. The existence and uniqueness of global smooth solutions is also proved for a regularization model of this simplified system.

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Mathematics Subject Classification: 35K55, 35Q30, 58E99, 76D05.

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