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On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs
Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate
1. | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China, China, China, China |
References:
[1] |
J. Carr, Applications of Centre Manifold Theory,, Springer Verlag, (1981).
|
[2] |
F. Chen, Introduction to Plasma Physics and Controlled Fusion,, Second edition, (1984). Google Scholar |
[3] |
D. Donatelli, Local and global existence for the coupled Navier-Stokes-Poisson problem,, Quart. Appl. Math., 61 (2003), 345.
|
[4] |
R. J. Duan and S. Q. Liu, Stability of rarefaction waves of the Navier-Stokes-Poisson system,, J. Differential Equations, 258 (2015), 2495.
doi: 10.1016/j.jde.2014.12.019. |
[5] |
R. J. Duan and S. Q. Liu, Stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann system,, SIAM J. Math. Anal., 47 (2015), 3585.
doi: 10.1137/140995179. |
[6] |
R. J. Duan, S. Q. Liu, H. Y. Yin and C. J. Zhu, Stability of the rarefaction wave for a two-fluid plasma model with diffusion,, Sci. China Math., 59 (2016), 67.
doi: 10.1007/s11425-015-5059-4. |
[7] |
R. J. Duan and X. F. Yang, Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations,, Comm. Pure Appl. Anal., 12 (2013), 985.
doi: 10.3934/cpaa.2013.12.985. |
[8] |
F. M. Huang and X. H. Qin, Stability of boundary layer and rarefaction wave to an outflow problem for compressible Navier-Stokes equations under large perturbation,, J. Differential Equations, 246 (2009), 4077.
doi: 10.1016/j.jde.2009.01.017. |
[9] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion,, Comm. Math. Phys., 101 (1985), 97.
doi: 10.1007/BF01212358. |
[10] |
S. Kawashima, T. Nakamura, S. Nishibata and P. C. Zhu, Stationary waves to viscous heat-conductive gases in half space: Existence, stability and convergence rate,, Math. Models Methods Appl. Sci., 20 (2010), 2201.
doi: 10.1142/S0218202510004908. |
[11] |
S. Kawashima, S. Nishibata and P. C. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space,, Comm. Math. Phys., 240 (2003), 483.
doi: 10.1007/s00220-003-0909-2. |
[12] |
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.
doi: 10.1007/s00205-009-0255-4. |
[13] |
S. Q. Liu, H. Y. Yin and C. J. Zhu, Stability of contact discontinuity for the Navier-Stokes-Poisson system with free boundary,, preprint, (). Google Scholar |
[14] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations,, Springer, (1990).
doi: 10.1007/978-3-7091-6961-2. |
[15] |
A. Matsumura and M. Mei, Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary,, Arch. Ration. Mech. Anal., 146 (1999), 1.
doi: 10.1007/s002050050134. |
[16] |
A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas,, Comm. Math. Phys., 222 (2001), 449.
doi: 10.1007/s002200100517. |
[17] |
T. Nakamura, S. Nishibata and T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line,, J. Differential Equations, 241 (2007), 94.
doi: 10.1016/j.jde.2007.06.016. |
[18] |
T. Nakamura and S. Nishibata, Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas,, Journal of Hyperbolic Differential Equations, 8 (2011), 651.
doi: 10.1142/S0219891611002524. |
[19] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws,, Funkcial. Ekvac., 41 (1998), 107.
|
[20] |
L. Z. Ruan, H. Y. Yin and C. J. Zhu, The stability of the superposition of rarefaction wave and contact discontinuity for the Navier-Stokes-Poisson system with free boundary,, preprint., (). Google Scholar |
[21] |
Z. Tan, T. Yang, H. J. Zhao and Q. Y. Zou, Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data,, SIAM J. Math. Anal., 45 (2013), 547.
doi: 10.1137/120876174. |
[22] |
H. Y. Yin, J. S. Zhang and C. J. Zhu, Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier-Stokes-Poisson system,, Nonlinear Analysis: Real World Applications, 31 (2016), 492.
doi: 10.1016/j.nonrwa.2016.01.020. |
[23] |
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.
doi: 10.1016/j.jde.2010.07.035. |
[24] |
F. Zhou and Y. P. Li, Convergence rate of solutions toward stationary solutions to the bipolar Navier-Stokes-Poisson equations in a half line,, Bound. Value Probl., 2013 (2013), 1.
doi: 10.1186/1687-2770-2013-124. |
show all references
References:
[1] |
J. Carr, Applications of Centre Manifold Theory,, Springer Verlag, (1981).
|
[2] |
F. Chen, Introduction to Plasma Physics and Controlled Fusion,, Second edition, (1984). Google Scholar |
[3] |
D. Donatelli, Local and global existence for the coupled Navier-Stokes-Poisson problem,, Quart. Appl. Math., 61 (2003), 345.
|
[4] |
R. J. Duan and S. Q. Liu, Stability of rarefaction waves of the Navier-Stokes-Poisson system,, J. Differential Equations, 258 (2015), 2495.
doi: 10.1016/j.jde.2014.12.019. |
[5] |
R. J. Duan and S. Q. Liu, Stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann system,, SIAM J. Math. Anal., 47 (2015), 3585.
doi: 10.1137/140995179. |
[6] |
R. J. Duan, S. Q. Liu, H. Y. Yin and C. J. Zhu, Stability of the rarefaction wave for a two-fluid plasma model with diffusion,, Sci. China Math., 59 (2016), 67.
doi: 10.1007/s11425-015-5059-4. |
[7] |
R. J. Duan and X. F. Yang, Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations,, Comm. Pure Appl. Anal., 12 (2013), 985.
doi: 10.3934/cpaa.2013.12.985. |
[8] |
F. M. Huang and X. H. Qin, Stability of boundary layer and rarefaction wave to an outflow problem for compressible Navier-Stokes equations under large perturbation,, J. Differential Equations, 246 (2009), 4077.
doi: 10.1016/j.jde.2009.01.017. |
[9] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion,, Comm. Math. Phys., 101 (1985), 97.
doi: 10.1007/BF01212358. |
[10] |
S. Kawashima, T. Nakamura, S. Nishibata and P. C. Zhu, Stationary waves to viscous heat-conductive gases in half space: Existence, stability and convergence rate,, Math. Models Methods Appl. Sci., 20 (2010), 2201.
doi: 10.1142/S0218202510004908. |
[11] |
S. Kawashima, S. Nishibata and P. C. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space,, Comm. Math. Phys., 240 (2003), 483.
doi: 10.1007/s00220-003-0909-2. |
[12] |
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.
doi: 10.1007/s00205-009-0255-4. |
[13] |
S. Q. Liu, H. Y. Yin and C. J. Zhu, Stability of contact discontinuity for the Navier-Stokes-Poisson system with free boundary,, preprint, (). Google Scholar |
[14] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations,, Springer, (1990).
doi: 10.1007/978-3-7091-6961-2. |
[15] |
A. Matsumura and M. Mei, Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary,, Arch. Ration. Mech. Anal., 146 (1999), 1.
doi: 10.1007/s002050050134. |
[16] |
A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas,, Comm. Math. Phys., 222 (2001), 449.
doi: 10.1007/s002200100517. |
[17] |
T. Nakamura, S. Nishibata and T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line,, J. Differential Equations, 241 (2007), 94.
doi: 10.1016/j.jde.2007.06.016. |
[18] |
T. Nakamura and S. Nishibata, Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas,, Journal of Hyperbolic Differential Equations, 8 (2011), 651.
doi: 10.1142/S0219891611002524. |
[19] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws,, Funkcial. Ekvac., 41 (1998), 107.
|
[20] |
L. Z. Ruan, H. Y. Yin and C. J. Zhu, The stability of the superposition of rarefaction wave and contact discontinuity for the Navier-Stokes-Poisson system with free boundary,, preprint., (). Google Scholar |
[21] |
Z. Tan, T. Yang, H. J. Zhao and Q. Y. Zou, Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data,, SIAM J. Math. Anal., 45 (2013), 547.
doi: 10.1137/120876174. |
[22] |
H. Y. Yin, J. S. Zhang and C. J. Zhu, Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier-Stokes-Poisson system,, Nonlinear Analysis: Real World Applications, 31 (2016), 492.
doi: 10.1016/j.nonrwa.2016.01.020. |
[23] |
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.
doi: 10.1016/j.jde.2010.07.035. |
[24] |
F. Zhou and Y. P. Li, Convergence rate of solutions toward stationary solutions to the bipolar Navier-Stokes-Poisson equations in a half line,, Bound. Value Probl., 2013 (2013), 1.
doi: 10.1186/1687-2770-2013-124. |
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