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Zero-electron-mass limit of Euler-Poisson equations
1. | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106 |
2. | Department of Mathematics, Zhejiang University, Hangzhou 310027 |
References:
[1] |
T. Alazard, Low mach number limit of the full Navier-Stokes equations, Arch. Ration. Mech. Anal., 180 (2006), 1-73.
doi: 10.1007/s00205-005-0393-2. |
[2] |
G. Alì, Global existence of smooth solutions of the N-dimensional Euler-Possion model, SIAM J. Math. Anal., 35 (2003), 389-422.
doi: 10.1137/S0036141001393225. |
[3] |
G. Alì and L. Chen, The zero-electron-mass limit in the Euler-Poisson system for both well- and ill-prepared initial data, Nonlinearity, 24 (2011), 2745-2761.
doi: 10.1088/0951-7715/24/10/005. |
[4] |
G. Alì, L. Chen, A. Jüngel and Y. J. Peng, The zero-electron-mass limit in the hydrodynamic model for plasmas, Nonlinear Anal. TMA, 72 (2010), 4415-4427.
doi: 10.1016/j.na.2010.02.016. |
[5] |
J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, "Mathematical Geophysics. An Introduction to Rotating Fluids and the Navier-Stokes Equations," Oxford Lecture Series in Mathematics and its Applications, 32. The Clarendon Press, Oxford University Press, Oxford, 2006 |
[6] |
L. Chen, X. Q. Chen and C. L. Zhang, Vanishing electron mass limit in the bipolar Euler-Poisson system, Nonlinear Anal. RWA, 12 (2011), 1002-1012.
doi: 10.1016/j.nonrwa.2010.08.023. |
[7] |
R. Danchin, Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, Ann. Sci. École Norm. Sup. (4), 35 (2002), 27-75.
doi: 10.1016/S0012-9593(01)01085-0. |
[8] |
P. Degond and P. A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Lett., 3 (1990), 25-29.
doi: 10.1016/0893-9659(90)90130-4. |
[9] |
D. Y. Fang, J. Xu and T. Zhang, Global exponential stability of classical solutions to the hydrodynamic model for semiconductors, Math. Models Methods Appl. Sci., 17 (2007), 1507-1530.
doi: 10.1142/S0218202507002364. |
[10] |
T. Goudon, A. Jüngel and Y. J. Peng, Zero-mass-electrons limits in hydrodynamic models for plasmas, Appl. Math. Lett., 12 (1999), 75-79.
doi: 10.1016/S0893-9659(99)00038-5. |
[11] |
Y. Guo and W. Strauss, Stability of semiconductor states with Insulating and contact boundary conditions, Arch. Rational Mech. Anal., 179 (2005), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[12] |
D. W. Hewett, Low-frequency electro-magnetic (Darwin) applications in plasma simulation, Comput. Phys. Commun., 84 (1994), 243-277. |
[13] |
L. Hsiao, S. Jiang and P. Zhang, Global existence and exponential stablity of smooth solutions to a full hydrodynamic model to semiconductors, Monatshefte f$\ddotu$r Mathematik, 136 (2002), 269-285.
doi: 10.1007/s00605-002-0485-0. |
[14] |
D. Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces, Rev. Mat. Iberoamericana, 15 (1999), 1-36.
doi: 10.4171/RMI/248. |
[15] |
A. Jüngel and Y. J. Peng, A hierarchy of hydrodynamic models for plasmas: Zero-electron-mass limits in the drift-diffusion equations, Ann. Inst. H. Poincaré Anal. NonLinéaire, 17 (2000), 83-118.
doi: 10.1016/S0294-1449(99)00101-8. |
[16] |
F. Kazeminezhad, J. M. Dawson, J. N. Leboeuf, R. Sydora and D. Holland, A vlasov particle ion zero mass electron model for plasma simulations, J. Comput. Phys., 102 (1992), 277-296.
doi: 10.1016/0021-9991(92)90372-6. |
[17] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[18] |
S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math., 35 (1982), 629-651.
doi: 10.1002/cpa.3160350503. |
[19] |
S. Kawashima and W. A. Yong, Dissipative structure and entropy for hyperbolic systems of balance laws, Arch. Ration. Mech. Anal., 174 (2004), 345-364.
doi: 10.1007/s00205-004-0330-9. |
[20] |
C. Lattanzio and P. Marcati, The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors, Discrete Contin. Dyn. Syst.-A, 5 (1999), 449-455.
doi: 10.3934/dcds.1999.5.449. |
[21] |
P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equations, Arch. Ration. Mech. Anal., 129 (1995), 129-145.
doi: 10.1007/BF00379918. |
[22] |
P. A. Markowich, C. Ringhofer and C. Schmeiser, "Semiconductor Equations," Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[23] |
G. Métivier and S. Schochet, The incompressible limit of the Non-Isentropic euler equations, Arch. Ration. Mech. Anal., 158 (2001), 61-90.
doi: 10.1007/PL00004241. |
[24] |
S. Wang, Quasineutral limit of Euler-Poisson system with and without viscosity, Comm. PDE, 29 (2004), 419-456.
doi: 10.1081/PDE-120030403. |
[25] |
J. Xu and W.-A. Yong, Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors, J. Diff. Equs., 247 (2009), 1777-1795.
doi: 10.1016/j.jde.2009.06.018. |
[26] |
J. Xu and W.-A. Yong, Zero-electron-mass limit of hydrodynamic models for plasmas, Proc. Roy. Soc. Edinburgh Sect. A, 141 (2011), 431-447.
doi: 10.1017/S0308210510000119. |
[27] |
W.-A. Yong, Diffusive relaxation limit of multi-dimensional isentropic hydrodynamic models for semiconductor, SIAM J. Appl. Math., 64 (2004), 1737-1748.
doi: 10.1137/S0036139903427404. |
[28] |
W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Ration. Mech. Anal., 172 (2004), 247-266.
doi: 10.1007/s00205-003-0304-3. |
show all references
References:
[1] |
T. Alazard, Low mach number limit of the full Navier-Stokes equations, Arch. Ration. Mech. Anal., 180 (2006), 1-73.
doi: 10.1007/s00205-005-0393-2. |
[2] |
G. Alì, Global existence of smooth solutions of the N-dimensional Euler-Possion model, SIAM J. Math. Anal., 35 (2003), 389-422.
doi: 10.1137/S0036141001393225. |
[3] |
G. Alì and L. Chen, The zero-electron-mass limit in the Euler-Poisson system for both well- and ill-prepared initial data, Nonlinearity, 24 (2011), 2745-2761.
doi: 10.1088/0951-7715/24/10/005. |
[4] |
G. Alì, L. Chen, A. Jüngel and Y. J. Peng, The zero-electron-mass limit in the hydrodynamic model for plasmas, Nonlinear Anal. TMA, 72 (2010), 4415-4427.
doi: 10.1016/j.na.2010.02.016. |
[5] |
J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, "Mathematical Geophysics. An Introduction to Rotating Fluids and the Navier-Stokes Equations," Oxford Lecture Series in Mathematics and its Applications, 32. The Clarendon Press, Oxford University Press, Oxford, 2006 |
[6] |
L. Chen, X. Q. Chen and C. L. Zhang, Vanishing electron mass limit in the bipolar Euler-Poisson system, Nonlinear Anal. RWA, 12 (2011), 1002-1012.
doi: 10.1016/j.nonrwa.2010.08.023. |
[7] |
R. Danchin, Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, Ann. Sci. École Norm. Sup. (4), 35 (2002), 27-75.
doi: 10.1016/S0012-9593(01)01085-0. |
[8] |
P. Degond and P. A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Lett., 3 (1990), 25-29.
doi: 10.1016/0893-9659(90)90130-4. |
[9] |
D. Y. Fang, J. Xu and T. Zhang, Global exponential stability of classical solutions to the hydrodynamic model for semiconductors, Math. Models Methods Appl. Sci., 17 (2007), 1507-1530.
doi: 10.1142/S0218202507002364. |
[10] |
T. Goudon, A. Jüngel and Y. J. Peng, Zero-mass-electrons limits in hydrodynamic models for plasmas, Appl. Math. Lett., 12 (1999), 75-79.
doi: 10.1016/S0893-9659(99)00038-5. |
[11] |
Y. Guo and W. Strauss, Stability of semiconductor states with Insulating and contact boundary conditions, Arch. Rational Mech. Anal., 179 (2005), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[12] |
D. W. Hewett, Low-frequency electro-magnetic (Darwin) applications in plasma simulation, Comput. Phys. Commun., 84 (1994), 243-277. |
[13] |
L. Hsiao, S. Jiang and P. Zhang, Global existence and exponential stablity of smooth solutions to a full hydrodynamic model to semiconductors, Monatshefte f$\ddotu$r Mathematik, 136 (2002), 269-285.
doi: 10.1007/s00605-002-0485-0. |
[14] |
D. Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces, Rev. Mat. Iberoamericana, 15 (1999), 1-36.
doi: 10.4171/RMI/248. |
[15] |
A. Jüngel and Y. J. Peng, A hierarchy of hydrodynamic models for plasmas: Zero-electron-mass limits in the drift-diffusion equations, Ann. Inst. H. Poincaré Anal. NonLinéaire, 17 (2000), 83-118.
doi: 10.1016/S0294-1449(99)00101-8. |
[16] |
F. Kazeminezhad, J. M. Dawson, J. N. Leboeuf, R. Sydora and D. Holland, A vlasov particle ion zero mass electron model for plasma simulations, J. Comput. Phys., 102 (1992), 277-296.
doi: 10.1016/0021-9991(92)90372-6. |
[17] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[18] |
S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math., 35 (1982), 629-651.
doi: 10.1002/cpa.3160350503. |
[19] |
S. Kawashima and W. A. Yong, Dissipative structure and entropy for hyperbolic systems of balance laws, Arch. Ration. Mech. Anal., 174 (2004), 345-364.
doi: 10.1007/s00205-004-0330-9. |
[20] |
C. Lattanzio and P. Marcati, The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors, Discrete Contin. Dyn. Syst.-A, 5 (1999), 449-455.
doi: 10.3934/dcds.1999.5.449. |
[21] |
P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equations, Arch. Ration. Mech. Anal., 129 (1995), 129-145.
doi: 10.1007/BF00379918. |
[22] |
P. A. Markowich, C. Ringhofer and C. Schmeiser, "Semiconductor Equations," Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[23] |
G. Métivier and S. Schochet, The incompressible limit of the Non-Isentropic euler equations, Arch. Ration. Mech. Anal., 158 (2001), 61-90.
doi: 10.1007/PL00004241. |
[24] |
S. Wang, Quasineutral limit of Euler-Poisson system with and without viscosity, Comm. PDE, 29 (2004), 419-456.
doi: 10.1081/PDE-120030403. |
[25] |
J. Xu and W.-A. Yong, Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors, J. Diff. Equs., 247 (2009), 1777-1795.
doi: 10.1016/j.jde.2009.06.018. |
[26] |
J. Xu and W.-A. Yong, Zero-electron-mass limit of hydrodynamic models for plasmas, Proc. Roy. Soc. Edinburgh Sect. A, 141 (2011), 431-447.
doi: 10.1017/S0308210510000119. |
[27] |
W.-A. Yong, Diffusive relaxation limit of multi-dimensional isentropic hydrodynamic models for semiconductor, SIAM J. Appl. Math., 64 (2004), 1737-1748.
doi: 10.1137/S0036139903427404. |
[28] |
W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Ration. Mech. Anal., 172 (2004), 247-266.
doi: 10.1007/s00205-003-0304-3. |
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