Work

Large-time behavior of pressureless Euler–Poisson equations with background states

Year: 2025

Type: article

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.

Source: Physica D Nonlinear Phenomena

DOI: 10.1016/j.physd.2025.134979

Authors: Young-Pil Choi, Dong-ha Kim, Dowan Koo, Eitan Tadmor

Institutions: Yonsei University, Chung-Ang University, University of Maryland, College Park

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,640