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On Fractional Schrödinger Equations in sobolev spaces
Large time behavior of solution for the full compressible navier-stokes-maxwell system
1. | Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai |
2. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P.R.China |
References:
[1] |
F. Chen, Introduction to Plasma Physics and Controlled Fusion, Vol. 1, Plenum Press, New York, 1984. |
[2] |
G. Q. Chen, J. W. Jerome and D. H. Wang, Compressible Euler-Maxwell equations, Transport Theory Statist. Phys., 29 (2000), 311-331.
doi: 10.1080/00411450008205877. |
[3] |
P. A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511626333. |
[4] |
R. J. Duan, Global smooth flows for the compressible Euler-Maxwell system: relaxation case, J. Hyperbolic Differ. Equ., 8 (2011), 375-413.
doi: 10.1142/S0219891611002421. |
[5] |
R. J. Duan, Green's function and large time behavior of the Navier-Stokes-Maxwell system, Anal. Appl. (Singap.), 10 (2012), 133-197.
doi: 10.1142/S0219530512500078. |
[6] |
Y. H. Feng, Y. J. Peng and S. Wang, Asymptotic behavior of global smooth solutions for full compressible Navier-Stokes-Maxwell equations, Nonlinear Anal. Real World Appl., 19 (2014), 105-116.
doi: 10.1016/j.nonrwa.2014.03.004. |
[7] |
Y. H. Feng, S. Wang and S. Kawashima, Global existence and asymptotic decay of solutions to the non-isentropic Euler-Maxwell system, Math. Models Methods Appl. Sci., 14 (2014), 2851-2884.
doi: 10.1142/S0218202514500390. |
[8] |
P. Germain and N. Masmoudi, Global existence for the Euler-Maxwell system, Ann. Sci. Éc. Norm. Supér., 3 (2014), 469-503. |
[9] |
Y. Guo, Smooth irrotational fluids in the large to the Euler-Poisson system in $\mathbbR^{3+1}$, Comm. Math. Phys., 195 (1998), 249-265.
doi: 10.1007/s002200050388. |
[10] |
M. L. Hajjej and Y. J. Peng, Initial layers and zero-relaxation limits of Euler-Maxwell equations, J. Differential Equations, 252 (2012), 1441-1465.
doi: 10.1016/j.jde.2011.09.029. |
[11] |
F.-M. Huang, M. Mei, Y. Wang and H.-M. Yu, Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors, SIAM J. Math. Anal., 43 (2011), 411-429.
doi: 10.1137/100793025. |
[12] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal., 58 (1975), 181-205. |
[13] |
S. Kawashima, System of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Manetohydrodynamics, Ph.D thesis, Kyoto University, Kyoto, 1983. |
[14] |
H. L. Li, A. Matsumura and G. J. Zhang, Optimal decay rate of the compressible Navier-Stokes-Poisson system in $\mathbbR^{3}$, Arch. Rational Mech. Anal., 196 (2010), 681-713.
doi: 10.1007/s00205-009-0255-4. |
[15] |
Q. Q. Liu and C. J. Zhu, Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations, Indiana Univ. Math. J., 4 (2013), 1203-1235.
doi: 10.1512/iumj.2013.62.5047. |
[16] |
T. P. Liu and W. K. Wang, The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd-multi dimensions, Comm. Math. Phys., 196 (1998), 145-173.
doi: 10.1007/s002200050418. |
[17] |
T. Luo, R. Natalini and Z. P. Xin, Large-time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math., 59 (1998), 810-830.
doi: 10.1137/S0036139996312168. |
[18] |
P. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[19] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to compressible Euler-Poisson equations, Chin. Ann. Math. Ser. B, 28 (2007), 583-602.
doi: 10.1007/s11401-005-0556-3. |
[20] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to incompressible Euler equations, Comm. Partial Differential Equations, 33 (2008), 349-376.
doi: 10.1080/03605300701318989. |
[21] |
Y. J. Peng and S. Wang, Rigorous derivation of incompressible e-MHD equations from compressible Euler-Maxwell equations, SIAM J. Math. Anal., 40 (2008), 540-565.
doi: 10.1137/070686056. |
[22] |
Y. Ueda and S. Kawashima, Decay property of regularity-loss type for the Euler-Maxwell system, Methods Appl. Anal., 18 (2011), 245-268.
doi: 10.4310/MAA.2011.v18.n3.a1. |
[23] |
Y. Ueda, S. Wang and S. Kawashima, Dissipative structure of the regularity type and time asymptotic decay of solutions for the Euler-Maxwell system, SIAM J. Math. Anal., 44 (2012), 2002-2017.
doi: 10.1137/100806515. |
[24] |
W. K. Wang and T. Yang, The pointwise estimates of solutions for Euler equations with damping in multi-dimension, J. Differential Equations, 173 (2001), 410-450.
doi: 10.1006/jdeq.2000.3937. |
[25] |
J. W. Yang, R. X. Lian and S. Wang, Incompressible type Euler as scaling limit of compressible Euler-Maxwell equations, Commun. Pure Appl. Anal., 1 (2013), 503-518.
doi: 10.3934/cpaa.2013.12.503. |
[26] |
J. W. Yang and S. Wang, Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations, Sci. China Math., 10 (2014), 2153-2162.
doi: 10.1007/s11425-014-4792-4. |
show all references
References:
[1] |
F. Chen, Introduction to Plasma Physics and Controlled Fusion, Vol. 1, Plenum Press, New York, 1984. |
[2] |
G. Q. Chen, J. W. Jerome and D. H. Wang, Compressible Euler-Maxwell equations, Transport Theory Statist. Phys., 29 (2000), 311-331.
doi: 10.1080/00411450008205877. |
[3] |
P. A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511626333. |
[4] |
R. J. Duan, Global smooth flows for the compressible Euler-Maxwell system: relaxation case, J. Hyperbolic Differ. Equ., 8 (2011), 375-413.
doi: 10.1142/S0219891611002421. |
[5] |
R. J. Duan, Green's function and large time behavior of the Navier-Stokes-Maxwell system, Anal. Appl. (Singap.), 10 (2012), 133-197.
doi: 10.1142/S0219530512500078. |
[6] |
Y. H. Feng, Y. J. Peng and S. Wang, Asymptotic behavior of global smooth solutions for full compressible Navier-Stokes-Maxwell equations, Nonlinear Anal. Real World Appl., 19 (2014), 105-116.
doi: 10.1016/j.nonrwa.2014.03.004. |
[7] |
Y. H. Feng, S. Wang and S. Kawashima, Global existence and asymptotic decay of solutions to the non-isentropic Euler-Maxwell system, Math. Models Methods Appl. Sci., 14 (2014), 2851-2884.
doi: 10.1142/S0218202514500390. |
[8] |
P. Germain and N. Masmoudi, Global existence for the Euler-Maxwell system, Ann. Sci. Éc. Norm. Supér., 3 (2014), 469-503. |
[9] |
Y. Guo, Smooth irrotational fluids in the large to the Euler-Poisson system in $\mathbbR^{3+1}$, Comm. Math. Phys., 195 (1998), 249-265.
doi: 10.1007/s002200050388. |
[10] |
M. L. Hajjej and Y. J. Peng, Initial layers and zero-relaxation limits of Euler-Maxwell equations, J. Differential Equations, 252 (2012), 1441-1465.
doi: 10.1016/j.jde.2011.09.029. |
[11] |
F.-M. Huang, M. Mei, Y. Wang and H.-M. Yu, Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors, SIAM J. Math. Anal., 43 (2011), 411-429.
doi: 10.1137/100793025. |
[12] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal., 58 (1975), 181-205. |
[13] |
S. Kawashima, System of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Manetohydrodynamics, Ph.D thesis, Kyoto University, Kyoto, 1983. |
[14] |
H. L. Li, A. Matsumura and G. J. Zhang, Optimal decay rate of the compressible Navier-Stokes-Poisson system in $\mathbbR^{3}$, Arch. Rational Mech. Anal., 196 (2010), 681-713.
doi: 10.1007/s00205-009-0255-4. |
[15] |
Q. Q. Liu and C. J. Zhu, Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations, Indiana Univ. Math. J., 4 (2013), 1203-1235.
doi: 10.1512/iumj.2013.62.5047. |
[16] |
T. P. Liu and W. K. Wang, The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd-multi dimensions, Comm. Math. Phys., 196 (1998), 145-173.
doi: 10.1007/s002200050418. |
[17] |
T. Luo, R. Natalini and Z. P. Xin, Large-time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math., 59 (1998), 810-830.
doi: 10.1137/S0036139996312168. |
[18] |
P. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[19] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to compressible Euler-Poisson equations, Chin. Ann. Math. Ser. B, 28 (2007), 583-602.
doi: 10.1007/s11401-005-0556-3. |
[20] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to incompressible Euler equations, Comm. Partial Differential Equations, 33 (2008), 349-376.
doi: 10.1080/03605300701318989. |
[21] |
Y. J. Peng and S. Wang, Rigorous derivation of incompressible e-MHD equations from compressible Euler-Maxwell equations, SIAM J. Math. Anal., 40 (2008), 540-565.
doi: 10.1137/070686056. |
[22] |
Y. Ueda and S. Kawashima, Decay property of regularity-loss type for the Euler-Maxwell system, Methods Appl. Anal., 18 (2011), 245-268.
doi: 10.4310/MAA.2011.v18.n3.a1. |
[23] |
Y. Ueda, S. Wang and S. Kawashima, Dissipative structure of the regularity type and time asymptotic decay of solutions for the Euler-Maxwell system, SIAM J. Math. Anal., 44 (2012), 2002-2017.
doi: 10.1137/100806515. |
[24] |
W. K. Wang and T. Yang, The pointwise estimates of solutions for Euler equations with damping in multi-dimension, J. Differential Equations, 173 (2001), 410-450.
doi: 10.1006/jdeq.2000.3937. |
[25] |
J. W. Yang, R. X. Lian and S. Wang, Incompressible type Euler as scaling limit of compressible Euler-Maxwell equations, Commun. Pure Appl. Anal., 1 (2013), 503-518.
doi: 10.3934/cpaa.2013.12.503. |
[26] |
J. W. Yang and S. Wang, Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations, Sci. China Math., 10 (2014), 2153-2162.
doi: 10.1007/s11425-014-4792-4. |
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