Stability of periodic steady-state solutions to a non-isentropic Euler–Maxwell system
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This paper is concerned with a stability problem in a periodic domain for a non-isentropic Euler–Maxwell system without temperature diffusion term. This system is used to describe the dynamics of electrons in magnetized plasmas when the ion density is a given smooth function which can be large. When the initial data are close to the steady states of the system, we show the global existence of smooth solutions which converge toward the steady states as the time tends to infinity. We make a change of unknown variables and choose a non-diagonal symmetrizer of the full Euler equations to get the dissipation estimates. We also adopt an induction argument on the order of derivatives of solutions in energy estimates to get the stability result.
KeywordsEuler–Maxwell system Global smooth solution Stability Steady-state solution Energy estimate
Mathematics Subject Classification35B40 35Q60 35Q35
- 9.Germain, P., Masmoudi, N.: Global existence for the Euler–Maxwell system. Ann. Sci. Ecole Norm. Supér. 47, fascicule 3, 469–503 (2014) Google Scholar
- 14.Lax, P.D.: Hyperbolic systems of conservation laws and the mathematical theory of shock waves, SIAM Regional Conf. Lecture, No. 11, Philadelphia, (1973)Google Scholar