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Energy conservative solutions to a nonlinear wave system of nematic liquid crystals
1.  Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States 
2.  Academy of Mathematics & Systems Science, and Hua LooKeng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China 
3.  Department of Mathematical Sciences, Yeshiva University, New York, NY 10033 
References:
[1] 
Giuseppe Alì and John Hunter, Orientation waves in a director field with rotational inertia,, Kinet. Relat. Models, 2 (2009), 1. Google Scholar 
[2] 
H. Berestycki, J. M. Coron and I. Ekeland (eds.), "Variational Methods,", in series, (). Google Scholar 
[3] 
A. Bressan and Yuxi Zheng, Conservative solutions to a nonlinear variational wave equation,, Comm. Math. Phys., 266 (2006), 471. Google Scholar 
[4] 
D. Christodoulou and A. TahvildarZadeh, On the regularity of spherically symmetric wave maps,, Comm. Pure Appl. Math., 46 (1993), 1041. Google Scholar 
[5] 
J. Coron, J. Ghidaglia and F. Hélein (eds.), "Nematics,", Kluwer Academic Publishers, (1991). Google Scholar 
[6] 
J. L. Ericksen and D. Kinderlehrer (eds.), "Theory and Application of Liquid Crystals,", IMA Volumes in Mathematics and its Applications, (). Google Scholar 
[7] 
James Glimm, Solutions in the large for nonlinear hyperbolic systems of equations,, Comm. Pure Appl. Math., 18 (1965), 697. Google Scholar 
[8] 
R. Hardt, D. Kinderlehrer and Fanghua Lin, Existence and partial regularity of static liquid crystal configurations,, Comm. Math. Phys., 105 (1986), 547. Google Scholar 
[9] 
D. Kinderlehrer, Recent developments in liquid crystal theory,, in, (1991), 151. Google Scholar 
[10] 
R. A. Saxton, Dynamic instability of the liquid crystal director,, in, (1989), 325. Google Scholar 
[11] 
J. Shatah, Weak solutions and development of singularities in the $SU(2)$ $\sigma$model,, Comm. Pure Appl. Math., 41 (1988), 459. Google Scholar 
[12] 
J. Shatah and A. TahvildarZadeh, Regularity of harmonic maps from Minkowski space into rotationally symmetric manifolds,, Comm. Pure Appl. Math., 45 (1992), 947. Google Scholar 
[13] 
J. Sterbenz and D. Tataru, Energy dispersed large data wave maps in $2+1$ dimensions,, Comm. Math. Phys., 298 (2010), 139. Google Scholar 
[14] 
J. Sterbenz and D. Tataru, Regularity of wavemaps in dimension $2+1$,, Comm. Math. Phys., 298 (2010), 231. Google Scholar 
[15] 
T. Tao, Global regularity of wave maps. I. Small critical Sobolev norm in high dimension,, Internat. Math. Res. Notices, 6 (2001), 299. Google Scholar 
[16] 
T. Tao, Global regularity of wave maps. II. Small energy in two dimensions,, Comm. Math. Phys., 224 (2001), 443. Google Scholar 
[17] 
E. Virga, "Variational Theories for Liquid Crystals,", Chapman & Hall, (1994). Google Scholar 
[18] 
Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation,, Arch. Ration. Mech. Anal., 166 (2003), 303. Google Scholar 
[19] 
Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation with general data,, Ann. I. H. Poincar\'e, 22 (2005), 207. Google Scholar 
[20] 
Ping Zhang and Yuxi Zheng, Conservative solutions to a system of variational wave equations of nematic liquid crystals,, Arch. Ration. Mech. Anal., 195 (2010), 701. Google Scholar 
[21] 
Ping Zhang and Yuxi Zheng, Energy conservative solutions to a onedimensional full variational wave system,, Comm. Pure Appl. Math., 65 (2012), 683. Google Scholar 
show all references
References:
[1] 
Giuseppe Alì and John Hunter, Orientation waves in a director field with rotational inertia,, Kinet. Relat. Models, 2 (2009), 1. Google Scholar 
[2] 
H. Berestycki, J. M. Coron and I. Ekeland (eds.), "Variational Methods,", in series, (). Google Scholar 
[3] 
A. Bressan and Yuxi Zheng, Conservative solutions to a nonlinear variational wave equation,, Comm. Math. Phys., 266 (2006), 471. Google Scholar 
[4] 
D. Christodoulou and A. TahvildarZadeh, On the regularity of spherically symmetric wave maps,, Comm. Pure Appl. Math., 46 (1993), 1041. Google Scholar 
[5] 
J. Coron, J. Ghidaglia and F. Hélein (eds.), "Nematics,", Kluwer Academic Publishers, (1991). Google Scholar 
[6] 
J. L. Ericksen and D. Kinderlehrer (eds.), "Theory and Application of Liquid Crystals,", IMA Volumes in Mathematics and its Applications, (). Google Scholar 
[7] 
James Glimm, Solutions in the large for nonlinear hyperbolic systems of equations,, Comm. Pure Appl. Math., 18 (1965), 697. Google Scholar 
[8] 
R. Hardt, D. Kinderlehrer and Fanghua Lin, Existence and partial regularity of static liquid crystal configurations,, Comm. Math. Phys., 105 (1986), 547. Google Scholar 
[9] 
D. Kinderlehrer, Recent developments in liquid crystal theory,, in, (1991), 151. Google Scholar 
[10] 
R. A. Saxton, Dynamic instability of the liquid crystal director,, in, (1989), 325. Google Scholar 
[11] 
J. Shatah, Weak solutions and development of singularities in the $SU(2)$ $\sigma$model,, Comm. Pure Appl. Math., 41 (1988), 459. Google Scholar 
[12] 
J. Shatah and A. TahvildarZadeh, Regularity of harmonic maps from Minkowski space into rotationally symmetric manifolds,, Comm. Pure Appl. Math., 45 (1992), 947. Google Scholar 
[13] 
J. Sterbenz and D. Tataru, Energy dispersed large data wave maps in $2+1$ dimensions,, Comm. Math. Phys., 298 (2010), 139. Google Scholar 
[14] 
J. Sterbenz and D. Tataru, Regularity of wavemaps in dimension $2+1$,, Comm. Math. Phys., 298 (2010), 231. Google Scholar 
[15] 
T. Tao, Global regularity of wave maps. I. Small critical Sobolev norm in high dimension,, Internat. Math. Res. Notices, 6 (2001), 299. Google Scholar 
[16] 
T. Tao, Global regularity of wave maps. II. Small energy in two dimensions,, Comm. Math. Phys., 224 (2001), 443. Google Scholar 
[17] 
E. Virga, "Variational Theories for Liquid Crystals,", Chapman & Hall, (1994). Google Scholar 
[18] 
Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation,, Arch. Ration. Mech. Anal., 166 (2003), 303. Google Scholar 
[19] 
Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation with general data,, Ann. I. H. Poincar\'e, 22 (2005), 207. Google Scholar 
[20] 
Ping Zhang and Yuxi Zheng, Conservative solutions to a system of variational wave equations of nematic liquid crystals,, Arch. Ration. Mech. Anal., 195 (2010), 701. Google Scholar 
[21] 
Ping Zhang and Yuxi Zheng, Energy conservative solutions to a onedimensional full variational wave system,, Comm. Pure Appl. Math., 65 (2012), 683. Google Scholar 
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