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The existence and blow-up criterion of liquid crystals system in critical Besov space

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  • We consider the existence of strong solution to liquid crystals system in critical Besov space, and give a criterion which is similar to Serrin's criterion on regularity of weak solution to Navier-Stokes equations.
    Mathematics Subject Classification: 76N10, 35Q35, 35Q30.


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  • [1]

    H. Bahouri, J. Y. Chemin and R. Danchin, "Fourier Analysis and Nonlinear Partial Differential Equations," Springer, 2011.


    R. Danchin, Global existence in critical spaces for compressible Navier-Stokes equations, Invent. Math., 141 (2000), 579-614.doi: 10.1007/s002220000078.


    R. Danchin, "Fourier Analysis Methods for PDE's," 2005. Available from: http://www.fichier-pdf.fr/2011/12/13/courschine/courschine.pdf.


    J. L. Ericksen, Hydrostatic theory of liquid crystals, Arch. Rational Mech. Anal., 9 (1962), 371-378.doi: 10.1007/BF00253358.


    H. Fujita and T. Kato, On the Navier-Stokes initial value problem I, Arch. Rational Mech. Anal., 16 (1964), 269-315.doi: 10.1007/BF00276188.


    M. C. Hong, Global existence of solutions of the simplified Ericksen–Leslie system in dimension two, Calc. Var., 40 (2011), 15-36.doi: 10.1007/s00526-010-0331-5.


    H. Kozono and Y. Shimada, Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations, Math. Nachr., 276 (2004), 63-74.doi: 10.1002/mana.200310213.


    F. M. Leslie, Some constitutive equations for liquid crystals, Arch. Rational Mech. Anal., 28 (1986), 265-283.doi: 10.1007/BF00251810.


    X. L. Li and D. H. Wang, Global solution to the incompressible flow of liquid crystals, J. Differential Equations, 252 (2012), 745-767.doi: 10.1016/j.jde.2011.08.045.


    F. H. Lin, Nonlinear theory of defects in nematic liquid crystals: Phase transition and flow phenomena, Comm. Pure Appl. Math., 1989, 42 (1989), 789-814.doi: 10.1002/cpa.3160420605.


    F. H. Lin and C. Liu, Partial regularity of the dynamic system modeling the flow of liquid crystals, Discrete Contin. Dyn. Syst. A, 2 (1998), 1-22.


    F. H. Lin and C. Liu, Nonparabolic dissipative systems modeling the flow of liquid crystals, Comm. Pure Appl. Math., XLVIII, 1995, 501-537.doi: 10.1002/cpa.3160480503.


    F. H. Lin and C. Liu, Existence of Solutions for the Ericksen-Leslie System, Arch. Rational Mech. Anal., 154 (2000), 135-156.doi: 10.1007/s002050000102.


    F. H. Lin, J. Y. Lin and C. Y. Wang, Liquid Crystal Flows in Two Dimensions, Arch. Rational Mech. Anal., 197 (2010), 297-336.doi: 10.1007/s00205-009-0278-x.


    J. Y. Lin and S. J. Ding, On the well-posedness for the heat flow of harmonic maps and the hydrodynamic flow of nematic liquid crystals in critical spaces, Math. Meth. Appl. Sci., 35 (2012), 158-173.doi: 10.1002/mma.1548.


    C. Y. Wang, Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data, Arch. Rational Mech. Anal., 200 (2011), 1-19.doi: 10.1007/s00205-010-0343-5.


    H. Wu, X. Xu and C. Liu, Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties, Calc. Var. Partial Differential Equations, 45 (2012), 319-345.doi: 10.1007/s00526-011-0460-5.

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