On dissipative solutions to a simplified hyperbolic Ericksen–Leslie system of liquid crystals

2021 ◽  
Vol 19 (1) ◽  
pp. 175-192
Author(s):  
Feng Cheng ◽  
Ning Jiang ◽  
Yi-Long Luo
2018 ◽  
Vol 15 (01) ◽  
pp. 15-35 ◽  
Author(s):  
Eduard Feireisl ◽  
Elisabetta Rocca ◽  
Giulio Schimperna ◽  
Arghir Zarnescu

We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution is proposed, for which a global-in-time existence theorem is shown. The dissipative solutions enjoy the following properties: (i) they exist globally in time for any finite energy initial data; (ii) dissipative solutions enjoying certain smoothness are classical solutions; (iii) a dissipative solution coincides with a strong solution originating from the same initial data as long as the latter exists.


Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1445-1456
Author(s):  
Bingyuan Huang

In the paper, we establish a Serrin type criterion for strong solutions to a simplified densitydependent Ericksen-Leslie system modeling incompressible, nematic liquid crystal materials in dimension three. The density may vanish in an open subset of ?. As a byproduct, we establish the Serrin type criterion for heat flow of harmonic map whose gradients belong to Lrx Lst, where 2/s + 3/r ? 1, for 3 < r ? ?.


Author(s):  
M. Locke ◽  
J. T. McMahon

The fat body of insects has always been compared functionally to the liver of vertebrates. Both synthesize and store glycogen and lipid and are concerned with the formation of blood proteins. The comparison becomes even more apt with the discovery of microbodies and the localization of urate oxidase and catalase in insect fat body.The microbodies are oval to spherical bodies about 1μ across with a depression and dense core on one side. The core is made of coiled tubules together with dense material close to the depressed membrane. The tubules may appear loose or densely packed but always intertwined like liquid crystals, never straight as in solid crystals (Fig. 1). When fat body is reacted with diaminobenzidine free base and H2O2 at pH 9.0 to determine the distribution of catalase, electron microscopy shows the enzyme in the matrix of the microbodies (Fig. 2). The reaction is abolished by 3-amino-1, 2, 4-triazole, a competitive inhibitor of catalase. The fat body is the only tissue which consistantly reacts positively for urate oxidase. The reaction product is sharply localized in granules of about the same size and distribution as the microbodies. The reaction is inhibited by 2, 6, 8-trichloropurine, a competitive inhibitor of urate oxidase.


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