article

Title: Asymptotic stability of the compressible Euler-Maxwell equations to Euler-Poisson equations

Authors: Changjiang Zhu, Qingqing Liu and Haiyan Yin

Issue: Volume 63 (2014), Issue 4, 1085-1108

Abstract:

$In this paper, we consider a one-dimensional Euler-Maxwell system with initial data whose behaviors at far fields $x\to\pm\infty$ are different. Inspired by the relationship between Euler-Maxwell and Euler-Poisson, we can prove that the one-dimensional Euler-Maxwell equation behaves time asymptotically to the corresponding Euler-Poisson equation studied by Huang, Mei, Wang, and Yu in [F.\:M. Huang, M. Mei, Y. Wang, and H.\:M. Yu \textit{Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors}, SIAM J. Math. Anal. \textbf{43} (2011), no. 1, 411--429]. Meanwhile, we obtain the global existence of solutions based on the energy method.$