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Existence results for compressible radiation hydrodynamic equations with vacuum
1. | Department of Mathematics and Key Lab of Scientific and Engineering Computing (MOE), Shanghai Jiao Tong University, Shanghai 200240 |
2. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
References:
[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. |
[2] |
Z. Chen and Y. Wang, The well-posedness of the Cauchy problem for the Navier-Stokes-Boltzmann equations in radiation hydrodynamics, Dissertation, Shanghai Jiao Tong University, 2012. |
[3] |
Y. Cho, H. Choe and H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids, J. Math. Pures Appl., 83 (2004), 243-275.
doi: 10.1016/j.matpur.2003.11.004. |
[4] |
Y. Cho and H. Kim, On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities, Manu. Math., 120 (2006), 91-129.
doi: 10.1007/s00229-006-0637-y. |
[5] |
Y. Cho and H. Kim, Existence results for viscous polytropic fluids with vacuum, J. Differential Equations, 228 (2006), 377-411.
doi: 10.1016/j.jde.2006.05.001. |
[6] |
Y. Cho and B. Jin, Blow-up of viscous heat-conducting compressible flows, J. Math. Anal. Appl., 320 (2006), 819-826.
doi: 10.1016/j.jmaa.2005.08.005. |
[7] |
H. Choe and H. Kim, Strong solutions of the Navier-Stokes equations for isentropic compressible fluids, J. Differential Equations, 190 (2003), 504-523.
doi: 10.1016/S0022-0396(03)00015-9. |
[8] |
B. Ducomet, E. Feireisl and Š. Nečasová, On a model in radiation hydrodynamics, Ann. Inst. H. Poincaré. (C) Non Line. Anal., 6 (2011), 797-812.
doi: 10.1016/j.anihpc.2011.06.002. |
[9] |
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. |
[10] |
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, 8 (2012), 219-260.
doi: 10.1007/s10231-010-0180-z. |
[11] |
G. Galdi, An Introduction to the Mathmatical Theorey of the Navier-Stokes Equations, Springer: New York, 1994.
doi: 10.1007/978-0-387-09620-9. |
[12] |
X. Huang, J. Li and Z. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Comm. Pure Appl. Math., 65 (2012), 549-585.
doi: 10.1002/cpa.21382. |
[13] |
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. |
[14] |
S. Jiang and X. Zhong, Local existence and fiinte-time blow-up in multidimensional radiation hydrodynamics, J. Math. Fluid Mech., 9 (2007), 543-64.
doi: 10.1007/s00021-005-0213-3. |
[15] |
R. Kippenhahn and A. Weigert, Stellar Structure and Evolution, Springer, Berlin, Heideberg, 1994. |
[16] |
Y. Li and S. Zhu, On regular solutions of the $3$-D compressible isentropic Euler-Boltzmann equations with vacuum, to appear in Discrete Contin. Dynam. Systems-A, 2015. |
[17] |
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. |
[18] |
T. Makino, S. Ukai and S. Kawashima, Sur la solution à support compact de equations d'Euler compressible, Japan. J. Appl. Math., 33 (1986), 249-257.
doi: 10.1007/BF03167100. |
[19] |
G. Pomrancing, The Equations of Radiation Hydrodynamics, Oxford: Pergamon, 1973. |
[20] |
J. Simon, Compact sets in $L^P(0,T;B)$, Ann. Mat. Pura. Appl, 146 (1986), 65-96.
doi: 10.1007/BF01762360. |
[21] |
R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland: Amsterdam, 1984. |
show all references
References:
[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. |
[2] |
Z. Chen and Y. Wang, The well-posedness of the Cauchy problem for the Navier-Stokes-Boltzmann equations in radiation hydrodynamics, Dissertation, Shanghai Jiao Tong University, 2012. |
[3] |
Y. Cho, H. Choe and H. Kim, Unique solvability of the initial boundary value problems for compressible viscous fluids, J. Math. Pures Appl., 83 (2004), 243-275.
doi: 10.1016/j.matpur.2003.11.004. |
[4] |
Y. Cho and H. Kim, On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities, Manu. Math., 120 (2006), 91-129.
doi: 10.1007/s00229-006-0637-y. |
[5] |
Y. Cho and H. Kim, Existence results for viscous polytropic fluids with vacuum, J. Differential Equations, 228 (2006), 377-411.
doi: 10.1016/j.jde.2006.05.001. |
[6] |
Y. Cho and B. Jin, Blow-up of viscous heat-conducting compressible flows, J. Math. Anal. Appl., 320 (2006), 819-826.
doi: 10.1016/j.jmaa.2005.08.005. |
[7] |
H. Choe and H. Kim, Strong solutions of the Navier-Stokes equations for isentropic compressible fluids, J. Differential Equations, 190 (2003), 504-523.
doi: 10.1016/S0022-0396(03)00015-9. |
[8] |
B. Ducomet, E. Feireisl and Š. Nečasová, On a model in radiation hydrodynamics, Ann. Inst. H. Poincaré. (C) Non Line. Anal., 6 (2011), 797-812.
doi: 10.1016/j.anihpc.2011.06.002. |
[9] |
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. |
[10] |
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, 8 (2012), 219-260.
doi: 10.1007/s10231-010-0180-z. |
[11] |
G. Galdi, An Introduction to the Mathmatical Theorey of the Navier-Stokes Equations, Springer: New York, 1994.
doi: 10.1007/978-0-387-09620-9. |
[12] |
X. Huang, J. Li and Z. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Comm. Pure Appl. Math., 65 (2012), 549-585.
doi: 10.1002/cpa.21382. |
[13] |
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. |
[14] |
S. Jiang and X. Zhong, Local existence and fiinte-time blow-up in multidimensional radiation hydrodynamics, J. Math. Fluid Mech., 9 (2007), 543-64.
doi: 10.1007/s00021-005-0213-3. |
[15] |
R. Kippenhahn and A. Weigert, Stellar Structure and Evolution, Springer, Berlin, Heideberg, 1994. |
[16] |
Y. Li and S. Zhu, On regular solutions of the $3$-D compressible isentropic Euler-Boltzmann equations with vacuum, to appear in Discrete Contin. Dynam. Systems-A, 2015. |
[17] |
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. |
[18] |
T. Makino, S. Ukai and S. Kawashima, Sur la solution à support compact de equations d'Euler compressible, Japan. J. Appl. Math., 33 (1986), 249-257.
doi: 10.1007/BF03167100. |
[19] |
G. Pomrancing, The Equations of Radiation Hydrodynamics, Oxford: Pergamon, 1973. |
[20] |
J. Simon, Compact sets in $L^P(0,T;B)$, Ann. Mat. Pura. Appl, 146 (1986), 65-96.
doi: 10.1007/BF01762360. |
[21] |
R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland: Amsterdam, 1984. |
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