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

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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 : 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 
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     author = {Peng, Yue-Jun},
     title = {Global existence and long-time behavior of smooth solutions of two-fluid {Euler{\textendash}Maxwell} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {737--759},
     publisher = {Elsevier},
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     year = {2012},
     doi = {10.1016/j.anihpc.2012.04.002},
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     zbl = {1251.35159},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.04.002/}
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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, Tome 29 (2012) no. 5, pp. 737-759. doi: 10.1016/j.anihpc.2012.04.002

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