Local well-posedness and small Deborah limit of a molecule-based $Q$-tensor system

Sirui  Li; Wei  Wang; Pingwen Zhang

doi:10.3934/dcdsb.2015.20.2611

Article Contents

2015, Volume 20, Issue 8: 2611-2655. Doi: 10.3934/dcdsb.2015.20.2611

This issue Previous Article Fully discrete finite element method based on second-order Crank-Nicolson/Adams-Bashforth scheme for the equations of motion of Oldroyd fluids of order one Next Article Analytic integrability of a class of planar polynomial differential systems

Local well-posedness and small Deborah limit of a molecule-based $Q$-tensor system

1.
School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871
2.
Beijing International Center for Mathematical Research, Peking University, Beijing, 100871
3.
LMAM, CAPT and School of Mathematical Sciences, Peking University, Beijing, 100871

Received: September 30, 2014

Revised: December 31, 2014

Published: September 2015

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Abstract

In this paper, we consider a hydrodynamic $Q$-tensor system for nematic liquid crystal flow, which is derived from Doi-Onsager molecular theory by the Bingham closure. We first prove the existence and uniqueness of local strong solution. Furthermore, by taking Deborah number goes to zero and using the Hilbert expansion method, we present a rigorous derivation from the molecule-based $Q$-tensor theory to the Ericksen-Leslie theory.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35A01, 76A15, 76D05.

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References

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