Citation: |
[1] |
C. Buet and B. Després, Asymptotic analysis of fluid models for the coupling of radiation hydrodynamics, J. Quant. Spectroscopy Rad. Transf., 85 (2004), 385-418.doi: 10.1016/S0022-4073(03)00233-4. |
[2] |
B. Ducomet, E. Feireisl and Š. Nečasová, On a model in radiation hydrodynamics, Ann. Inst. H. Poincaré. (C) Non Line. Anal., 28 (2011), 797-812.doi: 10.1016/j.anihpc.2011.06.002. |
[3] |
B. Ducomet and Š. Nečasová, Global weak solutions to the 1-D compressible Navier-Stokes equations with radiation, Commun. Math. Anal., 8 (2010), 23-65. |
[4] |
B. Ducomet and Š. Nečasová, Large time behavior of the motion of a viscous heat-conducting one-dimensional gas coupled to radiation, Annali di Matematica Pura ed Applicata , 191 (2012), 219-260.doi: 10.1007/s10231-010-0180-z. |
[5] |
P. Jiang and D. Wang, Formation of singularities of solutions to the three-dimensional Euler-Boltzmann equations in radiation hydrodynamics, Nonlinearity, 23 (2010), 809-821.doi: 10.1088/0951-7715/23/4/003. |
[6] |
S. Jiang and X. Zhong, Local existence and fiinte-time blow-up in multidimensional radiation hydrodynamics, J. Math. Fluid Mech., 9 (2007), 543-564.doi: 10.1007/s00021-005-0213-3. |
[7] |
R. Kippenhahn and A. Weigert, Stellar structure and Evolution, Springer, Berlin, Heidelberg, 1994. |
[8] |
P. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys., 5 (1964), 611-613.doi: 10.1063/1.1704154. |
[9] |
Y. Li and S. Zhu, Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum, J. Differential Equations, 256 (2014), 3943-3980.doi: 10.1016/j.jde.2014.03.007. |
[10] |
Y. Li and S. Zhu, Existence results for the compressible radiation hydrodynamics equations with vacuum, 2013, submitted, http://arxiv.org/abs/1312.5337. |
[11] |
T. Liu and T. Yang, Compressible Euler equations with vacuum, J. Differential Equations, 140 (1997), 223-237.doi: 10.1006/jdeq.1997.3281. |
[12] |
T. Liu, Compressible flow with damping and vacuum, Japan J. Indust. Appl. Math., 13 (1996), 25-32.doi: 10.1007/BF03167296. |
[13] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Science, 53, Spinger-Verlag, New York, 1984.doi: 10.1007/978-1-4612-1116-7. |
[14] |
T. Makino, Blowing up solutions of the Euler-Possion equation for the evolution of gaseous stars, Trans. Theo. Statist. Phys., 21 (1992), 615-624.doi: 10.1080/00411459208203801. |
[15] |
T. Makino, S. Ukai and S. Kawashima, Sur la solution à support compact de equations d'Euler compressible, Japan. J. Appl. Math., 3 (1986), 249-257.doi: 10.1007/BF03167100. |
[16] |
J. Neumann, Discussion on the Existence and Uniqueness or Multiplicity of Solutions of the Aerodynamical Equations, Collected works of J. Von Neumann, 1949. |
[17] |
G. Pomrancing, The Equations of Radiation Hydrodynamics, Oxford, Pergamon, 1973. |
[18] |
T. Sideris, T. Becca and D. Wang, Long time behavior of solutions to the 3D compressible Euler equations with Damping, Commun. Part. Differ. Equations, 28 (2003), 795-816.doi: 10.1081/PDE-120020497. |
[19] |
T. Sideris, Formation of singulirities in three-dimensional compressible fluids, Commun. Math. Phys., 101 (1985), 475-485.doi: 10.1007/BF01210741. |
[20] |
Z. Xin and W. Yan, On blow-up of classical solutions to the compressible Navier-Stokes Equations, Commun. Math. Phys., 321 (2013), 529-541.doi: 10.1007/s00220-012-1610-0. |
[21] |
C. Xu and T. Yang, Local existence with physical vacuum boundary condition to Euler equations with damping, J. Differertial Equations, 210 (2005), 217-231.doi: 10.1016/j.jde.2004.06.005. |