Spherically symmetric solutions to compressible hydrodynamic flow of liquid crystals in N dimensions

Jinrui Huang , Shijin Ding

Chinese Annals of Mathematics, Series B ›› 2012, Vol. 33 ›› Issue (3) : 453 -478.

PDF
Chinese Annals of Mathematics, Series B ›› 2012, Vol. 33 ›› Issue (3) : 453 -478. DOI: 10.1007/s11401-012-0706-3
Article

Spherically symmetric solutions to compressible hydrodynamic flow of liquid crystals in N dimensions

Author information +
History +
PDF

Abstract

The paper is concerned with the system modeling the compressible hydrodynamic flow of liquid crystals with radially symmetric initial data and non-negative initial density in dimension N (N ≥ 2). The authors obtain the existence of global radially symmetric strong solutions in a bounded or unbounded annular domain for any γ > 1.

Keywords

Liquid crystals / Compressible hydrodynamic flow / Global solutions

Cite this article

Download citation ▾
Jinrui Huang, Shijin Ding. Spherically symmetric solutions to compressible hydrodynamic flow of liquid crystals in N dimensions. Chinese Annals of Mathematics, Series B, 2012, 33(3): 453-478 DOI:10.1007/s11401-012-0706-3

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Caffarelli L., Kohn R., Nirenberg L.. First order interpolation inequalities with weights. Compositio Math, 1984, 53: 259-275

[2]

Cho Y. G., Choe H. J., Kim H.. Unique solvability of the initial boundary value problems for compressible viscous fluids. J. Math. Pures Appl., 2003, 83: 243-275

[3]

Choe H. J., Kim H.. Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fuids. Math. Meth. Appl. Sci., 2005, 28: 1-28

[4]

Ding, S. J., Huang, J. R., Wen, H. Y., et al., Incompressible limit of the compressible hydrodynamic Flow. arXiv: 1104.4377v1

[5]

Ding, S. J., Lin, J. Y., Wang, C. Y., et al., Compressible hydrodynamic flow of liquid crystals in 1-D, Discrete Contin. Dyn. Syst., to appear.

[6]

Ericksen J.. Hydrostatic theory of liquid crystal. Arch. Rational Mech. Anal., 1962, 9: 371-378

[7]

Fan J. S., Jiang S., Ni G. X.. Uniform boundedness of the radially symmetric solutions of the Navier-Stokes equations for isentropic compressible fluids. Osaka, J. Math., 2009, 46: 863-876

[8]

Guo B. L., Han Y. Q.. Global regular solutions for Landau-Lifshitz equation. Front. Math. China, 2006, 4: 538-568

[9]

Hoff D.. Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data. Indiana Univ. Math. J., 1992, 41: 1225-1302

[10]

Huang T., Wang C. Y., Wen H. Y.. Strong solutions of the compressible nematic liquid crystal flow. J. Diff. Eq., 2012, 252(3): 2222-2265

[11]

Jiang S., Zhang P.. On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations. Comm. Math. Phys., 2001, 215: 559-581

[12]

Ladyzenskaja O. A., Solonnikov V. A., Ural’ceva N. N.. Linear and quasilinear equations of parabolic type, 1968, Providence, RI: A. M. S.

[13]

Leslie F.. Some constitute equations for anisotropic fluids. Q. J. Mech. Appl. Math., 1966, 19: 357-370

[14]

Lin F. H.. Nonlinear theory of defects in nematic liquid crystal: phase transition and flow phenomena. Comm. Pure Appl. Math., 1989, 42: 789-814

[15]

Lin F. H., Lin J. Y., Wang C. Y.. Liquid crystal flows in dimensions two. Arch. Rat. Mech. Anal., 2010, 197: 297-336

[16]

Lin F. H., Liu C.. Nonparabolic dissipative systems modeling the flow of liquid crystals. Comm. Pure Appl. Math., 1995, 48: 501-537

[17]

Lin F. H., Liu C.. Partial regularities of the nonlinear dissipative systems modeling the flow of liquid crystals. DCDS, 1996, 2: 1-23

[18]

Lin F. H., Liu C.. Existence of solutions for the Ericksen-Leslie system. Arch. Rational Mech. Anal., 2000, 154: 135-156

[19]

Liu X. G., Zhang Z. Y.. Existence of the flow of liquid crystals system (in Chinese). Chin. Ann. Math., 2009, 30A(1): 1-20

[20]

Simon J.. Nonhomogeneous viscous incompressible fluids: existence of vecocity, density and pressure. SIAM J. Math. Anal., 1990, 21(5): 1093-1117

[21]

Valli A.. Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method. Ann. Scuola Norm. Sup. Pisa, 1983, 4: 607-647

[22]

Weigant V. A.. Example of non-existence in the large for the problem of the existence of solutions of Navier-Stokes equations for compressible viscous barotropic fluids. Dokl. Akad. Nauk., 1994, 339: 155-156

AI Summary AI Mindmap
PDF

127

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/