Partial regularity of a nematic liquid crystal model with kinematic transport effects

In this paper, we will establish the global existence of a suitable weak solution to the Erickson–Leslie system modelling hydrodynamics of nematic liquid crystal flows with kinematic transports for molecules of various shapes in R3 , which is smooth away from a closed set of (parabolic) Hausdorff dimension at most 157 .

[1]  J. Ericksen,et al.  Hydrostatic theory of liquid crystals , 1962 .

[2]  Fanghua Lin,et al.  Partial regularity of the dynamic system modeling the flow of liquid crystals , 1995 .

[3]  Fanghua Lin,et al.  A new proof of the Caffarelli‐Kohn‐Nirenberg theorem , 1998 .

[4]  Changyou Wang,et al.  Suitable Weak Solutions for the Co-rotational Beris–Edwards System in Dimension Three , 2019, Archive for Rational Mechanics and Analysis.

[5]  O. Ladyženskaja Linear and Quasilinear Equations of Parabolic Type , 1968 .

[6]  Benoit B. Mandelbrot,et al.  Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3+B , 1999 .

[7]  M. Giaquinta,et al.  Partial regularity for the solutions to nonlinear parabolic systems , 1973 .

[8]  Changyou Wang,et al.  Notes on the regularity of harmonic map systems , 2010 .

[9]  R. Kohn,et al.  Partial regularity of suitable weak solutions of the navier‐stokes equations , 1982 .

[10]  Fanghua Lin,et al.  Regularity and Existence of Global Solutions to the Ericksen–Leslie System in $${\mathbb{R}^2}$$R2 , 2013, 1305.5988.

[11]  J. Ericksen Liquid crystals with variable degree of orientation , 1991 .

[12]  F. M. Leslie Some constitutive equations for liquid crystals , 1968 .

[13]  A. Majda,et al.  Compressible and incompressible fluids , 1982 .

[14]  J. Ericksen Conservation Laws for Liquid Crystals , 1961 .

[15]  G. B. Jeffery The motion of ellipsoidal particles immersed in a viscous fluid , 1922 .

[16]  Chun Liu,et al.  Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties , 2009, 0901.1751.

[17]  HighWire Press Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character , 1934 .

[18]  F. Lin,et al.  Nonparabolic dissipative systems modeling the flow of liquid crystals , 1995 .

[19]  Petru Mironescu,et al.  Gagliardo–Nirenberg inequalities and non-inequalities: The full story , 2017, Annales de l'Institut Henri Poincaré C, Analyse non linéaire.

[20]  Petru Mironescu,et al.  Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces , 2001 .

[21]  Xiang Xu,et al.  On the General Ericksen–Leslie System: Parodi’s Relation, Well-Posedness and Stability , 2011, 1105.2180.