KdV limit of the Euler-Poisson system
arXiv:1202.1830 · doi:10.1007/s00205-013-0683-z
Abstract
Consider the scaling $\varepsilon^{1/2}(x-Vt)\to x,\ \varepsilon^{3/2}t\to t$ in the Euler-Poisson system for ion-acoustic waves \eqref{equ1}. We establish that as $\varepsilon\to 0$, the solutions to such Euler-Poisson system converge globally in time to the solutions of the Korteweg-de Vries equation.
35 pages, Several typos are replaced