American Institute of Mathematical Sciences

Advanced
January & February  2009, 23(1&2): 415-433. doi: 10.3934/dcds.2009.23.415

Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters

Yue-Jun Peng 1, and  Shu Wang 2,

1. 

Laboratoire de Mathématiques, CNRS UMR 6620, Université Clermont-Ferrand 2, 63177 Aubière cedex, France
2. 

College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100022

Received  December 2007 Revised  April 2008 Published  September 2008

This work is concerned with the two-fluid Euler-Maxwell equations for plasmas with small parameters. We study, by means of asymptotic expansions, the zero-relaxation limit, the non-relativistic limit and the combined non-relativistic and quasi-neutral limit. For each limit with well-prepared initial data, we show the existence and uniqueness of an asymptotic expansion up to any order. For general data, an asymptotic expansion up to order 1 of the non-relativistic limit is constructed by taking into account the initial layers. Finally, we discuss the justification of the limits.
Keywords: formal limits, initial layer expansion, Compressible Euler-Maxwell equations, asymptotic expansion.
Mathematics Subject Classification: 35B40, 35C20, 35L60, 35Q35.
Citation: Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415
[1]

Jianwei Yang, Ruxu Lian, Shu Wang. Incompressible type euler as scaling limit of compressible Euler-Maxwell equations. Communications on Pure & Applied Analysis, 2013, 12 (1) : 503-518. doi: 10.3934/cpaa.2013.12.503
[2]

Ju Ge, Wancheng Sheng. The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2733-2748. doi: 10.3934/cpaa.2014.13.2733
[3]

Xueke Pu, Min Li. Asymptotic behaviors for the full compressible quantum Navier-Stokes-Maxwell equations with general initial data. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 5149-5181. doi: 10.3934/dcdsb.2019055
[4]

Walter Allegretto, Liqun Cao, Yanping Lin. Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 543-576. doi: 10.3934/dcds.2008.20.543
[5]

Victor Wasiolek. Uniform global existence and convergence of Euler-Maxwell systems with small parameters. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2007-2021. doi: 10.3934/cpaa.2016025
[6]

Güher Çamliyurt, Igor Kukavica. A local asymptotic expansion for a solution of the Stokes system. Evolution Equations & Control Theory, 2016, 5 (4) : 647-659. doi: 10.3934/eect.2016023
[7]

Thierry Paul, Mario Pulvirenti. Asymptotic expansion of the mean-field approximation. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1891-1921. doi: 10.3934/dcds.2019080
[8]

Masahiro Suzuki. Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma. Kinetic & Related Models, 2016, 9 (3) : 587-603. doi: 10.3934/krm.2016008
[9]

Marissa Condon, Jing Gao, Arieh Iserles. On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4813-4837. doi: 10.3934/dcds.2016008
[10]

William Ott, Qiudong Wang. Periodic attractors versus nonuniform expansion in singular limits of families of rank one maps. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1035-1054. doi: 10.3934/dcds.2010.26.1035
[11]

Chengchun Hao. Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 2885-2931. doi: 10.3934/dcdsb.2015.20.2885
[12]

Shu Wang, Chundi Liu. Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2177-2199. doi: 10.3934/cpaa.2017108
[13]

Naoufel Ben Abdallah, Antoine Mellet, Marjolaine Puel. Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach. Kinetic & Related Models, 2011, 4 (4) : 873-900. doi: 10.3934/krm.2011.4.873
[14]

Sebastian J. Schreiber. Expansion rates and Lyapunov exponents. Discrete & Continuous Dynamical Systems - A, 1997, 3 (3) : 433-438. doi: 10.3934/dcds.1997.3.433
[15]

Matthieu Alfaro, Hiroshi Matano. On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1639-1649. doi: 10.3934/dcdsb.2012.17.1639
[16]

Kurusch Ebrahimi-Fard, Dominique Manchon. The tridendriform structure of a discrete Magnus expansion. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1021-1040. doi: 10.3934/dcds.2014.34.1021
[17]

Yan Guo, Juhi Jang, Ning Jiang. Local Hilbert expansion for the Boltzmann equation. Kinetic & Related Models, 2009, 2 (1) : 205-214. doi: 10.3934/krm.2009.2.205
[18]

Thomas Zaslavsky. Quasigroup associativity and biased expansion graphs. Electronic Research Announcements, 2006, 12: 13-18.

[19]

Young-Pil Choi. Compressible Euler equations interacting with incompressible flow. Kinetic & Related Models, 2015, 8 (2) : 335-358. doi: 10.3934/krm.2015.8.335
[20]

Shuxing Chen, Gui-Qiang Chen, Zejun Wang, Dehua Wang. A multidimensional piston problem for the Euler equations for compressible flow. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 361-383. doi: 10.3934/dcds.2005.13.361

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences