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- W2086843485 abstract "We consider a periodic problem for compressible Euler–Maxwell equations arising in the modeling of magnetized plasmas. The equations are quasilinear hyperbolic and partially dissipative. It is proved that smooth solutions exist globally in time and converge toward non-constant equilibrium states as the time goes to infinity. This result is obtained for initial data close to the equilibrium states with zero velocity. The proof is based on an induction argument on the order of the derivatives of solutions in energy and time dissipation estimates. We also show the global stability with exponential decay in time of solutions near the equilibrium states for compressible Euler–Poisson equations. On considère un problème périodique pour les équations d'Euler–Maxwell compressibles modélisant des plasmas magnétisés. Ces équations sont hyperboliques quasilinéaires et partiellement dissipatives. On démontre que les solutions régulières existent globalement en temps et convergent vers des états d'équilibre non constants lorsque le temps tend vers l'infini. Ce résultat est obtenu pour les données initiales proches des états d'équilibre avec vitesse nulle. La démonstration utilise un argument de récurrence sur l'ordre des dérivées des solutions dans des estimations d'énergie et de dissipation en temps. On montre aussi la stabilité globale avec décroissance exponentielle en temps des solutions proches des états d'équilibre pour les équations d'Euler–Poisson compressibles." @default.
- W2086843485 created "2016-06-24" @default.
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- W2086843485 date "2015-01-01" @default.
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- W2086843485 title "Stability of non-constant equilibrium solutions for Euler–Maxwell equations" @default.
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- W2086843485 doi "https://doi.org/10.1016/j.matpur.2014.03.007" @default.
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