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Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations. (English) Zbl 1251.35159
Summary: 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 don’t 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.

##### MSC:
 35Q60 PDEs in connection with optics and electromagnetic theory 35Q31 Euler equations 35Q05 Euler-Poisson-Darboux equations 35L45 Initial value problems for first-order hyperbolic systems 35B40 Asymptotic behavior of solutions to PDEs
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