| [1] |
Ding S J, Wang C Y, Wen H Y. Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one. Discrete Contin Dyn Syst Ser B, 2011, 15 : 357-371
doi: 10.3934/dcdsb.2011.15.357
|
| [2] |
Ding S J, Lin J Y, Wang C Y, Wen H Y. Compressible hydrodynamic flow of liquid crystals in 1-D. Discrete Contin Dyn Syst, 2012, 32 : 539-563
doi: 10.3934/dcds.2012.32.539
|
| [3] |
Ericksen J. Conservation laws for liquid crystals. Trans Soc Rheol, 1961, 5 : 23-34
|
| [4] |
Frid H, Shelukhin V V. Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry. SIAM J Math Anal, 2000, 31 : 1144-1156
doi: 10.1137/S003614109834394X
|
| [5] |
Hu X, Wu G. Global solution to the three-dimensional compressible flow of liquid crystals. SIAM J Math Anal, 2013, 45 (5): 2678-2699
doi: 10.1137/120898814
|
| [6] |
Huang T, Wang C, Wen H. Strong solutions of the compressible nematic liquid crystal flow. J Diff Eqs, 2012, 252 : 2222-2256
doi: 10.1016/j.jde.2011.07.036
|
| [7] |
Huang T, Wang C Y, Wen H Y. Blow up criterion for compressible nematic liquid crystal flows in dimension three. Arch Rat Mech Anal, 2012, 204 (1): 285-311
doi: 10.1007/s00205-011-0476-1
|
| [8] |
Jiang F, Jiang S, Wang D. On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain. J Funct Anal, 2013, 265 (12): 3369-3397
doi: 10.1016/j.jfa.2013.07.026
|
| [9] |
Jiang S, Zhang J W. Boundary layers for the Navier-Stokes equations of compressible heat-conducting flows with cylindrical symmetry. SIAM J Math Anal, 2009, 41 : 237-268
doi: 10.1137/07070005X
|
| [10] |
Li J, Xu Z, Zhang J. Global existence of classical solutions with large oscillations and vacuum to the three-dimensional compressible nematic liquid crystal flows. J Math Fluid Mech, 2018, 20 (4): 2105-2145
doi: 10.1007/s00021-018-0400-7
|
| [11] |
Lin J, Lai B, Wang C. Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three. SIAM J Math Anal, 2015, 47 (4): 2952-2983
doi: 10.1137/15M1007665
|
| [12] |
Liu Y. On the global existence of classical solutions for compressible nematic liquid crystal flows with vacuum. Z Angew Math Phys, 2020, 71 (1): 1-16
doi: 10.1007/s00033-019-1224-x
|
| [13] |
Liu Y, Zhong X. Global existence of strong solutions with large oscillations and vacuum to the compressible nematic liquid crystal flows in 3D bounded domains. arXiv:2204.06227
|
| [14] |
Qin X L, Yang T, Yao Z A, Zhou W S. Vanishing shear viscosity and boundary layer for the Navier-Stokes equations with cylindrical symmetry. Arch Ration Mech Anal, 2015, 216 (3): 1049-1086
doi: 10.1007/s00205-014-0826-x
|
| [15] |
Sun Y, Zhong X. Global strong solutions to the compressible nematic liquid crystal flows with large oscillations and vacuum in 2D bounded domains. J Geom Anal, 2023, 33 (10): Art 319
|
| [16] |
Tao Q, Gao J, Yao Z. Global strong solutions of the compressible nematic liquid crystal flow with the cylinder symmetry. Commun Math Sci, 2015, 13 (8): 2065-2096
doi: 10.4310/CMS.2015.v13.n8.a5
|
| [17] |
Wang Y H, Wen H Y, Zhang W H. Vanishing shear viscosity limit for the Navier-Stokes equations with cylindrical symmetry: boundary layer and optimal convergence rate. SIAM J Math Anal, 2023, 55 (3): 1631-1675
doi: 10.1137/22M1509321
|
| [18] |
Wang D, Yu C. Global weak solution and large-time behavior for the compressible flow of liquid crystals. Arch Ration Mech Anal, 2012, 204 (3): 881-915
doi: 10.1007/s00205-011-0488-x
|
| [19] |
Wang F, Zhong X. Global well-posedness to the compressible nematic liquid crystal flows with large oscillations and vacuum in 3D exterior domains. J Math Phys, 2023, 64 (2): Art 021505
|
| [20] |
Wen H, Yang T, Zhao X, Zhu C. Optimal convergence rate of the vanishing shear viscosity limit for compressible Navier-Stokes equations with cylindrical symmetry. J Math Pures Appl, 2021, 146 (9): 99-126
doi: 10.1016/j.matpur.2020.09.003
|
| [21] |
Wu G, Tan Z. Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals. J Diff Eqs, 2018, 264 (11): 6603-6632
doi: 10.1016/j.jde.2018.01.045
|
| [22] |
Yao L, Zhang T, Zhu C J. Boundary layers for compressible Navier-Stokes equations with density dependent viscosity and cylindrical symmetry. Ann Inst H Poincar Anal NonLinaire, 2011, 28 : 677-709
|
| [23] |
Ye X, Zhang J W. Boundary-layer phenomena for the cylindrically symmetric Navier-Stokes equations of compressible heat-conducting fluids with large data at vanishing shear viscosity. Nonlinearity, 2016, 29 (8): 2395-2416
doi: 10.1088/0951-7715/29/8/2395
|