关于可压液晶方程组的能量有界性
The Boundedness of Energy for Compressible Liquid Crystals System
摘要
考察可压液晶方程组有关能量的基本性质.证明了只要初始能量有界,此系统的能量就是一个与时间无关的有界量.
This paper concerns the general property of the energy function for compressible liquid crystals system.It is shown that the energy is bounded independent of time when the initial energy is bounded.
出处
《数学年刊(A辑)》
CSCD
北大核心
2011年第1期1-10,共10页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10631020,No.11071043)资助的项目
关键词
液晶
有界能量弱解
嵌入定理
Liquid crystal
Bounded energy weak solution
Embedding theorem
参考文献19
-
1Matsumura A, Nishida T. The initial value problem for the equations of motion of compressible viscous and heat-conductives fluids [J]. Proc Japan Acad Set A Math Sci, 1979, 55(9):337 342.
-
2Hoff D. Global solutions of the Navier-Stokes equations for multidimensional compress- ible flow with discontinuous initial data [J]. J Differential Equations, 1995, 120(1):215- 254.
-
3Hoff D. Strong convergence to global solutions for multidimentional flows of compress- ible, viscous fluids with polytropic equations of state and discontinuous initial data [J]. Arch Rational Mech Anal, 1995, 132(1):1 14.
-
4Lions P L. Mathematical topics in fluid dynamics, Vol 1: incompressible models Oxford: Oxford University Press, 1996.
-
5Lions P L. Mathematical topics in fluid dynamics, Vol 2: compressible models Oxford: Oxford University Press, 1998.
-
6Eduard Feireisl, Antonfn Novotny, Hana Petzeltova. On the existence of globally defined weak solutions to the Navier-Stokes equations [J]. J Math Fluid Mech, 2001, 3(4):358 :392.
-
7Erieksen J L. Conservation laws for liquid crystals [Jl. Trans Soc Rheology, 1961, 5:23 34.
-
8Ericksen J L. Continuum theory of nematic liquid crystals [J]. Res Mechanica, 1987 21:381-392.
-
9Leslie F M. On the thermodynamics of polar fluids [J]. Arch Rational Mech Anal, 1979, 70(2):189-202.
-
10Leslie F M. Some constitutive equations for liquid crystals [J]. Arch Rational Mech Anal, 1968, 28(4):265-283.
二级参考文献15
-
1Ericksen J. L., Hydrostatic theory of liquid crystals [J], Arch. Rational Mech. Anal., 1962, 9:371-378.
-
2Ericksen J. L. and Kinderlehrer D., Theory and Applications of Liquid Crystals [M], IMA Vol. 5, New York: Springer-Verlag, 1986.
-
3Leslie F. M., Some contitutive aligns for anisotropic fluids [J], Quart. J. Mech. Appl. Math., 1966, 19:357 370.
-
4Lin Fanghua, Nonlinear theory of defects in nematic liquid crystals: phase transition and flow phenomena [J], Comm. Pure Appl. Math., 1989, 42:789-814.
-
5Lin Fanghua and Liu Chun, Nonparabolic dissipative systems modeling the flow of liquid crystals [J], Comm. Pure Appl. Math., 1995, 48:501 537.
-
6Lin Fanghua and Liu Chun, Existence of solutions for the Ericksen-Leslie system [J], Arch. Rational Mech. Anal., 2000, 154:135-156.
-
7Lin Fanghua and Liu Chun, Partial regularities of the nonlinear dissipative systems modeling the flow of liquid crystals [J], Discrete and Continuous Dynamic Systems, 1996, 2:1-23.
-
8Feireisl E., Novotny A. and Petzeltova H., On the existence of globally defined weak solutions to the Navier-Stokes equations [J], J. Math. Fluid Mech., 2001, 3:358-392.
-
9Lions Pierrelouis, Mathematical Topics in Fluid Mechanics, Vol. 1, Incompressible Models [M], Oxford: Oxford Science Publication, 1996.
-
10Lions Pierrelouis, Mathematical Topics in Fluid Mechanics, Vol. 2, Compressible Models [M], Oxford: Oxford Science Publication, 1998.