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Large time behavior of solutions to the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbb{R}^{3}$
1. | School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China, China, China |
References:
[1] |
K. Deckelnick, $L^2$-decay for the compressible Navier-Stokes equations in unbounded domains, Comm. Partial Differential Equations, 18 (1993), 1445-1476.
doi: 10.1080/03605309308820981. |
[2] |
D. Donatelli, Local and global existence for the coupled Navier-Stokes-Poisson problem, Quart. Appl. Math, 61 (2003), 345-361. |
[3] |
B. Ducomet and A. Zlotnik, Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system, Appl. Math. Lett., 18 (2005), 1190-1198.
doi: 10.1016/j.aml.2004.12.002. |
[4] |
B. Ducomet, A remark about global existence for the Navier-Stokes-Poisson system, Appl. Math. Lett., 12 (1999), 31-37.
doi: 10.1016/S0893-9659(99)00098-1. |
[5] |
B. Ducomet, E. Feireisl, H. Petzeltová and I. Straškraba, Global in time weak solution for compressible barotropic self-gravitating fluids, Discrete Contin. Dyn. Syst, 11 (2004), 113-130.
doi: 10.3934/dcds.2004.11.113. |
[6] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, to appear in Commun. Part. Diff. Equ., 2012. |
[7] |
C. Hao and H.-L. Li, Global existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions, J. Differential Equation, 246 (2009), 4791-4812.
doi: 10.1016/j.jde.2008.11.019. |
[8] |
L. Hsiao, H.-L. Li, T. Yang and C. Zou, Compressible non-isentropic bipolar Navier-Stokes-Poisson system in $\mathbbR^3$, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 2169-2194. |
[9] |
D. L. Li, The Green's function of the Navier-Stokes equations for gas dynamics in $\mathbbR^3$, Comm. Math. Phy., 257 (2005), 579-619.
doi: 10.1007/s00220-005-1351-4. |
[10] |
H.-L. Li, A. Matsumura and G.-J. Zhang, Optimal decay rate of the compressible Navier-Stokes-Poisson system in $\mathbbR^3$, Arch. Ration. Mech. Anal., 196 (2010), 681-713.
doi: 10.1007/s00205-009-0255-4. |
[11] |
H.-L. Li, T. Yang and C. Zou, Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system, Acta Math. Sci. Ser. B Engl. Ed., 29 (2009), 1721-1736. |
[12] |
H.-L. Li and T. Zhang, Large time behavior of isentropic compressible Navier-Stokes system in $\mathbbR^3$, Math. Methods Appl. Sci., 34 (2011), 670-682.
doi: 10.1002/mma.1391. |
[13] |
H.-L. Li and T. Zhang, Large time behavior of solutions to $3D$ compressible Navier-Stokes-Poisson system, Sci. China Math., 55 (2012), 159-177.
doi: 10.1007/s11425-011-4280-z. |
[14] |
P. A. Markowich, C. A. Ringhofer and C. Schimeiser, "Semiconductor,'' Springer, 1990. |
[15] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A Math. Sci., 55 (1979), 337-342.
doi: 10.3792/pjaa.55.337. |
[16] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[17] |
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of motion of viscous and heat-conductive fluids, Comm. Math. Phys., 89 (1983), 445-464.
doi: 10.1007/BF01214738. |
[18] |
V. A. Solonnikov, Evolution free boundary problem for equations of motion viscous compressible self gravitating fluid, Stability Appl. Anal. Contin. Media, 3 (1993), 257-275. |
[19] |
Z. Tan and G. C. Wu, Global existence for the non-isentropic compressible Navier-Stokes-Poisson system in three and higher dimensions, Nonlinear Anal. Real World Appl., 13 (2012), 650-664.
doi: 10.1016/j.nonrwa.2011.08.005. |
[20] |
Y. J. Wang, Decay of the Navier-Stokes-Poisson equations, J. Diff. Equ., 253 (2012), 273-297.
doi: 10.1016/j.jde.2012.03.006. |
[21] |
G.-J. Zhang, H.-L. Li and C.-J. Zhu, Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbbR^3$, J. Differential Equations, 250 (2011), 866-891.
doi: 10.1016/j.jde.2010.07.035. |
[22] |
Y.-H. Zhang and Z. Tan, On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow, Math. Methods Appl. Sci., 30 (2007), 305-329.
doi: 10.1002/mma.786. |
show all references
References:
[1] |
K. Deckelnick, $L^2$-decay for the compressible Navier-Stokes equations in unbounded domains, Comm. Partial Differential Equations, 18 (1993), 1445-1476.
doi: 10.1080/03605309308820981. |
[2] |
D. Donatelli, Local and global existence for the coupled Navier-Stokes-Poisson problem, Quart. Appl. Math, 61 (2003), 345-361. |
[3] |
B. Ducomet and A. Zlotnik, Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system, Appl. Math. Lett., 18 (2005), 1190-1198.
doi: 10.1016/j.aml.2004.12.002. |
[4] |
B. Ducomet, A remark about global existence for the Navier-Stokes-Poisson system, Appl. Math. Lett., 12 (1999), 31-37.
doi: 10.1016/S0893-9659(99)00098-1. |
[5] |
B. Ducomet, E. Feireisl, H. Petzeltová and I. Straškraba, Global in time weak solution for compressible barotropic self-gravitating fluids, Discrete Contin. Dyn. Syst, 11 (2004), 113-130.
doi: 10.3934/dcds.2004.11.113. |
[6] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, to appear in Commun. Part. Diff. Equ., 2012. |
[7] |
C. Hao and H.-L. Li, Global existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions, J. Differential Equation, 246 (2009), 4791-4812.
doi: 10.1016/j.jde.2008.11.019. |
[8] |
L. Hsiao, H.-L. Li, T. Yang and C. Zou, Compressible non-isentropic bipolar Navier-Stokes-Poisson system in $\mathbbR^3$, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 2169-2194. |
[9] |
D. L. Li, The Green's function of the Navier-Stokes equations for gas dynamics in $\mathbbR^3$, Comm. Math. Phy., 257 (2005), 579-619.
doi: 10.1007/s00220-005-1351-4. |
[10] |
H.-L. Li, A. Matsumura and G.-J. Zhang, Optimal decay rate of the compressible Navier-Stokes-Poisson system in $\mathbbR^3$, Arch. Ration. Mech. Anal., 196 (2010), 681-713.
doi: 10.1007/s00205-009-0255-4. |
[11] |
H.-L. Li, T. Yang and C. Zou, Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system, Acta Math. Sci. Ser. B Engl. Ed., 29 (2009), 1721-1736. |
[12] |
H.-L. Li and T. Zhang, Large time behavior of isentropic compressible Navier-Stokes system in $\mathbbR^3$, Math. Methods Appl. Sci., 34 (2011), 670-682.
doi: 10.1002/mma.1391. |
[13] |
H.-L. Li and T. Zhang, Large time behavior of solutions to $3D$ compressible Navier-Stokes-Poisson system, Sci. China Math., 55 (2012), 159-177.
doi: 10.1007/s11425-011-4280-z. |
[14] |
P. A. Markowich, C. A. Ringhofer and C. Schimeiser, "Semiconductor,'' Springer, 1990. |
[15] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A Math. Sci., 55 (1979), 337-342.
doi: 10.3792/pjaa.55.337. |
[16] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[17] |
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of motion of viscous and heat-conductive fluids, Comm. Math. Phys., 89 (1983), 445-464.
doi: 10.1007/BF01214738. |
[18] |
V. A. Solonnikov, Evolution free boundary problem for equations of motion viscous compressible self gravitating fluid, Stability Appl. Anal. Contin. Media, 3 (1993), 257-275. |
[19] |
Z. Tan and G. C. Wu, Global existence for the non-isentropic compressible Navier-Stokes-Poisson system in three and higher dimensions, Nonlinear Anal. Real World Appl., 13 (2012), 650-664.
doi: 10.1016/j.nonrwa.2011.08.005. |
[20] |
Y. J. Wang, Decay of the Navier-Stokes-Poisson equations, J. Diff. Equ., 253 (2012), 273-297.
doi: 10.1016/j.jde.2012.03.006. |
[21] |
G.-J. Zhang, H.-L. Li and C.-J. Zhu, Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbbR^3$, J. Differential Equations, 250 (2011), 866-891.
doi: 10.1016/j.jde.2010.07.035. |
[22] |
Y.-H. Zhang and Z. Tan, On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow, Math. Methods Appl. Sci., 30 (2007), 305-329.
doi: 10.1002/mma.786. |
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