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The Cauchy problem on the compressible two-fluids Euler-Maxwell equations. (English) Zbl 1236.35116

Summary: We are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and the time-decay rates of perturbed solutions in \(L^q\) space for \(2\leq q\leq \infty\) are obtained. The proof for existence is due to the classical energy method, and the investigation of large-time behavior is based on linearized analysis of one-fluid Euler-Maxwell equations and damped Euler equations. As a byproduct of our approach, some time-decay rates obtained by T. C. Sideris, B. Thomases and D. Wang [Commun. Partial Differ. Equations 28, No. 3–4, 795–816 (2003; Zbl 1048.35051)] for the nonlinear damped Euler system are improved.

MSC:

35Q31 Euler equations
35Q60 PDEs in connection with optics and electromagnetic theory
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B40 Asymptotic behavior of solutions to PDEs

Citations:

Zbl 1048.35051
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