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One dimensional $p$-th power Newtonian fluid with temperature-dependent thermal conductivity
1. | School of Mathematics and Statistics, Wuhan University, Wuhan 430072 |
References:
[1] |
S. N. Antontsev, A. V. Kazhikhov and V. N. Monakhov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, North-Holland Publishing Co., Amsterdam, 1990. |
[2] |
S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases, 3rd edition, Cambridge University Press, Cambridge, 1990. |
[3] |
G. Q. Chen, Global solutions to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal., 23 (1992), 609-634.
doi: 10.1137/0523031. |
[4] |
H. Cui and Z.-A. Yao, Asymptotic behavior of compressible $p$-th power Newtonian fluid with large initial data, J. Differential Equations, 258 (2015), 919-953.
doi: 10.1016/j.jde.2014.10.011. |
[5] |
H. K. Jenssen and T. K. Karper, One-dimensional compressible flow with temperature dependent transport coefficients, SIAM J. Math. Anal., 42 (2010), 904-930.
doi: 10.1137/090763135. |
[6] |
J. I. Kanel', A model system of equations for the one-dimensional motion of a gas, Differencial$'$ nye Uravnenija, 4 (1968), 721-734. |
[7] |
S. Kawashima and M. Okada, Smooth global solutions for the one-dimensional equations in magnetohydrodynamics, Proc. Japan Acad. Ser. A Math. Sci., 58 (1982), 384-387. |
[8] |
A. V. Kazhikhov, On the Cauchy problem for the equations of a viscous gas, Sibirsk. Mat. Zh., 23 (1982), 60-64. |
[9] |
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, Prikl. Mat. Meh., 41 (1977), 282-291. |
[10] |
M. Lewicka and P. B. Mucha, On temporal asymptotics for the $p$th power viscous reactive gas, Nonlinear Anal., 57 (2004), 951-969.
doi: 10.1016/j.na.2003.12.001. |
[11] |
M. Lewicka and S. J. Watson, Temporal asymptotics for the $p$'th power Newtonian fluid in one space dimension, Z. Angew. Math. Phys., 54 (2003), 633-651.
doi: 10.1007/s00033-003-1149-1. |
[12] |
H. Liu, T. Yang, H. Zhao and Q. Zou, One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data, SIAM J. Math. Anal., 46 (2014), 2185-2228.
doi: 10.1137/130920617. |
[13] |
R. Pan and W. Zhang, Compressible Navier-Stokes equations with temperature dependent heat conductivity, Commun. Math. Sci., 13 (2015), 401-425.
doi: 10.4310/CMS.2015.v13.n2.a7. |
[14] |
Y. Qin and L. Huang, Global existence and exponential stability for the $p$th power viscous reactive gas, Nonlinear Anal., 73 (2010), 2800-2818.
doi: 10.1016/j.na.2010.06.015. |
[15] |
Y. Qin and L. Huang, Regularity and exponential stability of the $p$th Newtonian fluid in one space dimension, Math. Models Methods Appl. Sci., 20 (2010), 589-610.
doi: 10.1142/S0218202510004350. |
[16] |
Z. Tan, T. Yang, H. Zhao and Q. Zou, Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data, SIAM J. Math. Anal., 45 (2013), 547-571.
doi: 10.1137/120876174. |
show all references
References:
[1] |
S. N. Antontsev, A. V. Kazhikhov and V. N. Monakhov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, North-Holland Publishing Co., Amsterdam, 1990. |
[2] |
S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases, 3rd edition, Cambridge University Press, Cambridge, 1990. |
[3] |
G. Q. Chen, Global solutions to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal., 23 (1992), 609-634.
doi: 10.1137/0523031. |
[4] |
H. Cui and Z.-A. Yao, Asymptotic behavior of compressible $p$-th power Newtonian fluid with large initial data, J. Differential Equations, 258 (2015), 919-953.
doi: 10.1016/j.jde.2014.10.011. |
[5] |
H. K. Jenssen and T. K. Karper, One-dimensional compressible flow with temperature dependent transport coefficients, SIAM J. Math. Anal., 42 (2010), 904-930.
doi: 10.1137/090763135. |
[6] |
J. I. Kanel', A model system of equations for the one-dimensional motion of a gas, Differencial$'$ nye Uravnenija, 4 (1968), 721-734. |
[7] |
S. Kawashima and M. Okada, Smooth global solutions for the one-dimensional equations in magnetohydrodynamics, Proc. Japan Acad. Ser. A Math. Sci., 58 (1982), 384-387. |
[8] |
A. V. Kazhikhov, On the Cauchy problem for the equations of a viscous gas, Sibirsk. Mat. Zh., 23 (1982), 60-64. |
[9] |
A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, Prikl. Mat. Meh., 41 (1977), 282-291. |
[10] |
M. Lewicka and P. B. Mucha, On temporal asymptotics for the $p$th power viscous reactive gas, Nonlinear Anal., 57 (2004), 951-969.
doi: 10.1016/j.na.2003.12.001. |
[11] |
M. Lewicka and S. J. Watson, Temporal asymptotics for the $p$'th power Newtonian fluid in one space dimension, Z. Angew. Math. Phys., 54 (2003), 633-651.
doi: 10.1007/s00033-003-1149-1. |
[12] |
H. Liu, T. Yang, H. Zhao and Q. Zou, One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data, SIAM J. Math. Anal., 46 (2014), 2185-2228.
doi: 10.1137/130920617. |
[13] |
R. Pan and W. Zhang, Compressible Navier-Stokes equations with temperature dependent heat conductivity, Commun. Math. Sci., 13 (2015), 401-425.
doi: 10.4310/CMS.2015.v13.n2.a7. |
[14] |
Y. Qin and L. Huang, Global existence and exponential stability for the $p$th power viscous reactive gas, Nonlinear Anal., 73 (2010), 2800-2818.
doi: 10.1016/j.na.2010.06.015. |
[15] |
Y. Qin and L. Huang, Regularity and exponential stability of the $p$th Newtonian fluid in one space dimension, Math. Models Methods Appl. Sci., 20 (2010), 589-610.
doi: 10.1142/S0218202510004350. |
[16] |
Z. Tan, T. Yang, H. Zhao and Q. Zou, Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data, SIAM J. Math. Anal., 45 (2013), 547-571.
doi: 10.1137/120876174. |
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