Duan, Renjun; Liu, Qingqing; Zhu, Changjiang The Cauchy problem on the compressible two-fluids Euler-Maxwell equations. (English) Zbl 1236.35116 SIAM J. Math. Anal. 44, No. 1, 102-133 (2012). 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. Cited in 27 Documents 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 Keywords:bipolar Euler-Maxwell system; plasma physics; Euler equation with damping; time-decay rate Citations:Zbl 1048.35051 PDFBibTeX XMLCite \textit{R. Duan} et al., SIAM J. Math. Anal. 44, No. 1, 102--133 (2012; Zbl 1236.35116) Full Text: DOI