Large-time behavior of pressureless Euler--Poisson equations with background states
Abstract
We study the large-time asymptotic behavior of solutions to the one-dimensional damped pressureless Euler-Poisson system with variable background states, subject to a neutrality condition. In the case where the background density converges asymptotically to a positive constant, we establish the convergence of global classical solutions toward the corresponding equilibrium state. The proof combines phase plane analysis with hypocoercivity-type estimates. As an application, we analyze the damped pressureless Euler--Poisson system arising in cold plasma ion dynamics, where the electron density is modeled by a Maxwell-Boltzmann relation. We show that solutions converge exponentially to the steady state under suitable a priori bounds on the density and velocity fields. Our results provide a rigorous characterization of asymptotic stability for damped Euler-Poisson systems with nontrivial background structures.
Cite
@article{arxiv.2506.07812,
title = {Large-time behavior of pressureless Euler--Poisson equations with background states},
author = {Young-Pil Choi and Dong-ha Kim and Dowan Koo and Eitan Tadmor},
journal= {arXiv preprint arXiv:2506.07812},
year = {2025}
}