Global existence and long-time behavior of smooth solutions of two-fluid Euler–Maxwell equations
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, p. 737-759

We consider Cauchy problems and periodic problems for two-fluid compressible Euler–Maxwell equations arising in the modeling of magnetized plasmas. These equations are symmetrizable hyperbolic in the sense of Friedrichs but donʼt satisfy the so-called Kawashima stability condition. For both problems, we prove the global existence and long-time behavior of smooth solutions near a given constant equilibrium state. As a byproduct, we obtain similar results for two-fluid compressible Euler–Poisson equations.

DOI : https://doi.org/10.1016/j.anihpc.2012.04.002
Classification:  35L45,  35L60,  35Q60
Keywords: Two-fluid flows, Euler–Maxwell equations, Partially dissipative hyperbolic systems, Global smooth solutions, Long-time behavior, Energy estimates
@article{AIHPC_2012__29_5_737_0,
     author = {Peng, Yue-Jun},
     title = {Global existence and long-time behavior of smooth solutions of two-fluid Euler--Maxwell equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {5},
     year = {2012},
     pages = {737-759},
     doi = {10.1016/j.anihpc.2012.04.002},
     zbl = {1251.35159},
     mrnumber = {2971029},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_5_737_0}
}
Peng, Yue-Jun. Global existence and long-time behavior of smooth solutions of two-fluid Euler–Maxwell equations. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, pp. 737-759. doi : 10.1016/j.anihpc.2012.04.002. http://www.numdam.org/item/AIHPC_2012__29_5_737_0/

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