Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid
Abstract
We study the Cauchy problem for a three-dimensional bipolar Euler--Poisson system in which one fluid is pressureless and undamped, while the other is subject to momentum relaxation. For sufficiently small smooth perturbations of a constant equilibrium, we prove the global existence and uniqueness of smooth solutions under an irrotationality assumption on the initial velocity of the pressureless fluid, together with algebraic time-decay estimates. The main difficulty is that the velocity of the pressureless fluid is dissipated only indirectly through the Poisson coupling, and this mechanism degenerates strongly at high frequencies, leading to a regularity-loss structure. We overcome this difficulty by combining refined Green-function estimates, a low--middle--high frequency decomposition, and high-order nonlinear energy estimates adapted to the asymmetric regularity hierarchy. The result establishes a global small-data theory for this asymmetric regime, in which pressure and damping are simultaneously absent from the same fluid.
Related
- On one-dimensional pressureless Euler--Poisson systems: existence for non-semiconvex interaction potentials
- Global existence for the semilinear regular Euler-Poisson-Darboux-Tricomi equation, II
- Global Existence and Scattering of a Class of Two-Dimensional Euler--Poisson--Korteweg Systems
- Global Existence of Strong and Weak Solutions to the 2D Compressible Navier-Stokes-Poisson System in Bounded Domains with Large Data and Vacuum
- Perturbation Analysis of Gravitational Collapse of Gaseous Stars in the Pressureless Euler-Poisson System
BibTeX
@misc{choi2026global,
title = {{Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid}},
author = {Young-Pil Choi and Houzhi Tang and Weiyuan Zou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10959},
eprint = {2609.10959},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10959},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid
AU - Young-Pil Choi
AU - Houzhi Tang
AU - Weiyuan Zou
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.10959
UR - https://arxiv.org/abs/2609.10959
AB - We study the Cauchy problem for a three-dimensional bipolar Euler--Poisson system in which one fluid is pressureless and undamped, while the other is subject to momentum relaxation. For sufficiently small smooth perturbations of a constant equilibrium, we prove the global existence and uniqueness of smooth solutions under an irrotationality assumption on the initial velocity of the pressureless fluid, together with algebraic time-decay estimates. The main difficulty is that the velocity of the pressureless fluid is dissipated only indirectly through the Poisson coupling, and this mechanism degenerates strongly at high frequencies, leading to a regularity-loss structure. We overcome this difficulty by combining refined Green-function estimates, a low--middle--high frequency decomposition, and high-order nonlinear energy estimates adapted to the asymmetric regularity hierarchy. The result establishes a global small-data theory for this asymmetric regime, in which pressure and damping are simultaneously absent from the same fluid.
ER -