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Quasineutral limit of the Euler-Poisson system under strong magnetic fields
1. | Department of Mathematics, Chongqing University, Chongqing 401331 |
References:
[1] |
Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations, 25 (2000), 737-754.
doi: 10.1080/03605300008821529. |
[2] |
S. Cordier and E. Grenier, Quasineutral limit of an Euler-Poisson system arising from plasma physics, Comm. Partial Differential Equations, 25 (2000), 1099-1113.
doi: 10.1080/03605300008821542. |
[3] |
D. Gérard-Varet, D. Han-Kwan and F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries, Indiana Univ. Math. J., 62 (2013), 359-402.
doi: 10.1512/iumj.2013.62.4900. |
[4] |
F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with strong magnetic field in quasineutral regime, Math. Models Methods Appl. Sci., 13 (2003), 661-714.
doi: 10.1142/S0218202503002647. |
[5] |
Y. Guo and X. Pu, KdV limit of the Euler-Poisson system, Arch. Rational Mech. Anal., 211 (2014), 673-710.
doi: 10.1007/s00205-013-0683-z. |
[6] |
D. Han-Kwan, Quasineutral limit of the Vlasov-Poisson system with massless electrons, Comm. Partial Differential Equations, 36 (2011), 1385-1425.
doi: 10.1080/03605302.2011.555804. |
[7] |
Q. Ju, F. Li and H. Li, The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data, J. Differential Equations, 247 (2009), 203-224.
doi: 10.1016/j.jde.2009.02.019. |
[8] |
D. Lannes, F. Linares and J.-C. Saut, The Cauchy problem for the Euler-Poisson system and derivation of the Zakharov-Kuznetsov equation, Studies in Phase Space Analysis with Applications to PDEs, in Progress in Nonlinear Differential Equations and Their Applications, 84 (2013), 181-213.
doi: 10.1007/978-1-4614-6348-1_10. |
[9] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53, Springer-Verlag, New York-Berlin, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[10] |
Y. Peng and S. Wang, Convergence of compressible Euler-Poisson equations to incompressible type Euler equations, Asympt. Anal., 41 (2005), 141-160. |
[11] |
Y. Peng, S. Wang and Q. Gu, Relaxation limit and global existence of smooth solutions of compressible Euler-Maxwell equations, SIAM J. Math. Anal., 43 (2011), 944-970.
doi: 10.1137/100786927. |
[12] |
X. Pu, Dispersive limit of the Euler-Poisson system in higher dimensions, SIAM J. Math. Anal., 45 (2013), 834-878.
doi: 10.1137/120875648. |
[13] |
X. Pu and B. Guo, Quasineutral limit of the pressureless Euler-Poisson equation for ions, Quart. Appl. Math., 74 (2016), 245-273.
doi: 10.1090/qam/1424. |
[14] |
S. Wang, Quasineutral limit of Euler-Poisson system with and withour viscosity, Commun. Partial Differential Equations, 29 (2004), 419-456.
doi: 10.1081/PDE-120030403. |
[15] |
S. Wang and S. Jiang, The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations, 31 (2006), 571-591.
doi: 10.1080/03605300500361487. |
show all references
References:
[1] |
Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations, 25 (2000), 737-754.
doi: 10.1080/03605300008821529. |
[2] |
S. Cordier and E. Grenier, Quasineutral limit of an Euler-Poisson system arising from plasma physics, Comm. Partial Differential Equations, 25 (2000), 1099-1113.
doi: 10.1080/03605300008821542. |
[3] |
D. Gérard-Varet, D. Han-Kwan and F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries, Indiana Univ. Math. J., 62 (2013), 359-402.
doi: 10.1512/iumj.2013.62.4900. |
[4] |
F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with strong magnetic field in quasineutral regime, Math. Models Methods Appl. Sci., 13 (2003), 661-714.
doi: 10.1142/S0218202503002647. |
[5] |
Y. Guo and X. Pu, KdV limit of the Euler-Poisson system, Arch. Rational Mech. Anal., 211 (2014), 673-710.
doi: 10.1007/s00205-013-0683-z. |
[6] |
D. Han-Kwan, Quasineutral limit of the Vlasov-Poisson system with massless electrons, Comm. Partial Differential Equations, 36 (2011), 1385-1425.
doi: 10.1080/03605302.2011.555804. |
[7] |
Q. Ju, F. Li and H. Li, The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data, J. Differential Equations, 247 (2009), 203-224.
doi: 10.1016/j.jde.2009.02.019. |
[8] |
D. Lannes, F. Linares and J.-C. Saut, The Cauchy problem for the Euler-Poisson system and derivation of the Zakharov-Kuznetsov equation, Studies in Phase Space Analysis with Applications to PDEs, in Progress in Nonlinear Differential Equations and Their Applications, 84 (2013), 181-213.
doi: 10.1007/978-1-4614-6348-1_10. |
[9] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53, Springer-Verlag, New York-Berlin, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[10] |
Y. Peng and S. Wang, Convergence of compressible Euler-Poisson equations to incompressible type Euler equations, Asympt. Anal., 41 (2005), 141-160. |
[11] |
Y. Peng, S. Wang and Q. Gu, Relaxation limit and global existence of smooth solutions of compressible Euler-Maxwell equations, SIAM J. Math. Anal., 43 (2011), 944-970.
doi: 10.1137/100786927. |
[12] |
X. Pu, Dispersive limit of the Euler-Poisson system in higher dimensions, SIAM J. Math. Anal., 45 (2013), 834-878.
doi: 10.1137/120875648. |
[13] |
X. Pu and B. Guo, Quasineutral limit of the pressureless Euler-Poisson equation for ions, Quart. Appl. Math., 74 (2016), 245-273.
doi: 10.1090/qam/1424. |
[14] |
S. Wang, Quasineutral limit of Euler-Poisson system with and withour viscosity, Commun. Partial Differential Equations, 29 (2004), 419-456.
doi: 10.1081/PDE-120030403. |
[15] |
S. Wang and S. Jiang, The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations, 31 (2006), 571-591.
doi: 10.1080/03605300500361487. |
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