Smooth expanding planar simple waves for Euler--Poisson--Boltzmann: uniform stability and quasineutral expansion
Abstract
We study the warm-ion Euler--Poisson system with Maxwell--Boltzmann electrons on the cylinder R×T in the quasineutral regime. Taking a smooth expanding planar simple wave of the effective Euler system as the reference state, we construct an even Debye expansion through arbitrary finite order M with a residual of O(eps2M+2). We rigorously establish nonlinear stability on every fixed interval [t0,T] (t0≥0), achieving a lifespan and energy constants strictly independent of the Debye length 0<eps≤eps0. To overcome the singular scaling of the electric field, we develop a novel compensated energy topology that couples the warm-ion symmetrizer to the time-differentiated nonlinear Poisson constraint. By integrating the top-order electric work directly into the time derivative of a weighted energy functional, this mechanism controls the potential in Hs and its gradient in eps Hs, completely eliminating the eps−1 loss typically encountered in the momentum equation. This framework successfully governs distinct neutral end states, captures genuinely two-dimensional rotational perturbations, and yields an arbitrary-order quasineutral asymptotic expansion for prepared data, providing a critical analytical foundation for the geometric theory of multidimensional quasineutral rarefactions.
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BibTeX
@misc{wang2026smooth,
title = {{Smooth expanding planar simple waves for Euler--Poisson--Boltzmann: uniform stability and quasineutral expansion}},
author = {Louis Shuo Wang and Jiguang Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01589},
eprint = {2609.01589},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01589},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Smooth expanding planar simple waves for Euler--Poisson--Boltzmann: uniform stability and quasineutral expansion
AU - Louis Shuo Wang
AU - Jiguang Yu
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.01589
UR - https://arxiv.org/abs/2609.01589
AB - We study the warm-ion Euler--Poisson system with Maxwell--Boltzmann electrons on the cylinder R×T in the quasineutral regime. Taking a smooth expanding planar simple wave of the effective Euler system as the reference state, we construct an even Debye expansion through arbitrary finite order M with a residual of O(eps^2M+2). We rigorously establish nonlinear stability on every fixed interval [t_0,T] (t_0≥0), achieving a lifespan and energy constants strictly independent of the Debye length 0<eps≤eps_0. To overcome the singular scaling of the electric field, we develop a novel compensated energy topology that couples the warm-ion symmetrizer to the time-differentiated nonlinear Poisson constraint. By integrating the top-order electric work directly into the time derivative of a weighted energy functional, this mechanism controls the potential in H^s and its gradient in eps H^s, completely eliminating the eps^−1 loss typically encountered in the momentum equation. This framework successfully governs distinct neutral end states, captures genuinely two-dimensional rotational perturbations, and yields an arbitrary-order quasineutral asymptotic expansion for prepared data, providing a critical analytical foundation for the geometric theory of multidimensional quasineutral rarefactions.
ER -