# American Institute of Mathematical Sciences

April  2013, 33(4): 1499-1511. doi: 10.3934/dcds.2013.33.1499

## Partial regularity of minimum energy configurations in ferroelectric liquid crystals

 1 Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seadaemun-gu, Seoul 120-749, South Korea 2 Department of Mathematics, Chungnam National University, 99 Daehak-ro, Gung-Dong Yuseong-gu, Daejeon 305-764, South Korea

Received  July 2011 Revised  September 2012 Published  October 2012

Considered here is a system of smectic liquid crystals possessing polarizations described by the Oseen-Frank and Chen-Lubensky energies. We establish partial regularity of minimizers for the governing energy functional using the idea of $(c,\beta)$-almost minimizer introduced in [9].
Citation: Kyungkeun Kang, Jinhae Park. Partial regularity of minimum energy configurations in ferroelectric liquid crystals. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1499-1511. doi: 10.3934/dcds.2013.33.1499
##### References:

show all references

##### References:
 [1] Fanghua Lin, Chun Liu. Partial regularity of the dynamic system modeling the flow of liquid crystals. Discrete & Continuous Dynamical Systems, 1996, 2 (1) : 1-22. doi: 10.3934/dcds.1996.2.1 [2] Zhaoyang Qiu, Yixuan Wang. Martingale solution for stochastic active liquid crystal system. Discrete & Continuous Dynamical Systems, 2021, 41 (5) : 2227-2268. doi: 10.3934/dcds.2020360 [3] Bagisa Mukherjee, Chun Liu. On the stability of two nematic liquid crystal configurations. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 561-574. doi: 10.3934/dcdsb.2002.2.561 [4] M. Gregory Forest, Hongyun Wang, Hong Zhou. Sheared nematic liquid crystal polymer monolayers. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 497-517. doi: 10.3934/dcdsb.2009.11.497 [5] Domenico Mucci. Maps into projective spaces: Liquid crystal and conformal energies. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 597-635. doi: 10.3934/dcdsb.2012.17.597 [6] Guji Tian, Xu-Jia Wang. Partial regularity for elliptic equations. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 899-913. doi: 10.3934/dcds.2010.28.899 [7] Juan Dávila, Olivier Goubet. Partial regularity for a Liouville system. Discrete & Continuous Dynamical Systems, 2014, 34 (6) : 2495-2503. doi: 10.3934/dcds.2014.34.2495 [8] Eric P. Choate, Hong Zhou. Optimization of electromagnetic wave propagation through a liquid crystal layer. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 303-312. doi: 10.3934/dcdss.2015.8.303 [9] Zhenlu Cui, M. Carme Calderer, Qi Wang. Mesoscale structures in flows of weakly sheared cholesteric liquid crystal polymers. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 291-310. doi: 10.3934/dcdsb.2006.6.291 [10] Shanshan Guo, Zhong Tan. Energy dissipation for weak solutions of incompressible liquid crystal flows. Kinetic & Related Models, 2015, 8 (4) : 691-706. doi: 10.3934/krm.2015.8.691 [11] Jihong Zhao, Qiao Liu, Shangbin Cui. Global existence and stability for a hydrodynamic system in the nematic liquid crystal flows. Communications on Pure & Applied Analysis, 2013, 12 (1) : 341-357. doi: 10.3934/cpaa.2013.12.341 [12] Chun Liu, Huan Sun. On energetic variational approaches in modeling the nematic liquid crystal flows. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 455-475. doi: 10.3934/dcds.2009.23.455 [13] T. Tachim Medjo. On the existence and uniqueness of solution to a stochastic simplified liquid crystal model. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2243-2264. doi: 10.3934/cpaa.2019101 [14] Chun Liu, Jie Shen. On liquid crystal flows with free-slip boundary conditions. Discrete & Continuous Dynamical Systems, 2001, 7 (2) : 307-318. doi: 10.3934/dcds.2001.7.307 [15] Qiang Tao, Ying Yang. Exponential stability for the compressible nematic liquid crystal flow with large initial data. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1661-1669. doi: 10.3934/cpaa.2016007 [16] Patricia Bauman, Daniel Phillips. Analysis and stability of bent-core liquid crystal fibers. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1707-1728. doi: 10.3934/dcdsb.2012.17.1707 [17] Xiaoli Li, Boling Guo. Well-posedness for the three-dimensional compressible liquid crystal flows. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1913-1937. doi: 10.3934/dcdss.2016078 [18] Zhenlu Cui, Qi Wang. Permeation flows in cholesteric liquid crystal polymers under oscillatory shear. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 45-60. doi: 10.3934/dcdsb.2011.15.45 [19] Sili Liu, Xinhua Zhao, Yingshan Chen. A new blowup criterion for strong solutions of the compressible nematic liquid crystal flow. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4515-4533. doi: 10.3934/dcdsb.2020110 [20] M. Carme Calderer, Carlos A. Garavito Garzón, Baisheng Yan. A Landau--de Gennes theory of liquid crystal elastomers. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 283-302. doi: 10.3934/dcdss.2015.8.283

2020 Impact Factor: 1.392

## Metrics

• HTML views (0)
• Cited by (1)

• on AIMS