Acta mathematica scientia, Series B >
INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM
Received date: 2012-01-05
Online published: 2013-05-20
Supported by
This is work supported by National Natural Science Foundation of China -NSAF: 11071043, 11131005.
This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space RN and a bounded domain of RN with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.
HAO Yi-Hang , LIU Xian-Gao . INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 781 -796 . DOI: 10.1016/S0252-9602(13)60038-7
[1] Lions P L, Masmoudi N. Incompressible Limit for a Viscous Compressible Fluid. J Math Pures Appl, 1998, 77: 585–627
[2] Desjardins B, Grenier E, Lions P L, Masmoudi N. Incompressible Limit for Solutions of the Isentropic Navier-Stokes Equations with Dirichlet Boundary Conditions. J Math Pures Appl, 1999, 78: 461–471
[3] Desjardins B, Grenier E. Low Mach Number Limit of Viscous Compressible Flows in the Whole Space. Proc R Soc Lond A, 1999, 455: 2271–2279
[4] Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Applied
Mathematical Sciences, 53, 1984
[5] Lions P L. Mathematical Topics in Fluid Dynamics. Vol 2. Compressible models. Oxford: Oxford Science Publication, 1998
[6] Temam R. Navier-Stokes Equations. Rev Ed. Studies in Mathematics and its Applications 2. North-Holland: Amsterdam, 1977
[7] Garofalon N, Seg`ala F. Another step toward the solution of the Pompeiu problem in the plane. Comm Partial Differential Equations, 1993, 18: 491–503
[8] Evans L C. Partial Differential Equations//Graduate Studies in Mathematics 19. Providence: Amer Math Soc, 1998
[9] Feireisl E. Dynamics of Viscous Compressible Fluids. Oxford: Oxford University Press, 2004
[10] Chu Y M, Hao Y H, Liu X G. Global Weak Solutions to a General Liquid Crystals System. Discrete and Continuous Dynamical System -A, 2013, 33: 2681–2710
[11] Liu X G, Qing J. Globally Weak Solutions to the Flow of Compressible Liquid Crystals System. Discrete and Continuous Dynamical System -A, 2013, 33: 757–788
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