Large time behavior of global solutions to one-dimensional non-isentropic compressible Navier-Stokes-Poisson equations with large initial data
Abstract
In this paper, we are concerned with the construction of global solutions to the Cauchy problem for the one-dimensional non-isentropic compressible Navier-Stokes-Poisson equations, as well as the precise description of their large-time behavior. While results for small initial data are well-established, the case of large initial perturbations remains less satisfactory. Even for constant transport coefficients, only the Nishida-Smoller type solutions have been obtained so far. In this work, we will provide a complete resolution of this problem. The key idea involves revealing favorable hidden identities of the potential force and a new representation for the specific volume, which enables us to derive uniform upper and lower bounds on this quantity. Moreover, this strategy extends to compressible viscous single-ion flow under the Boltzmann relation; notably, this new method for deriving lower and upper bounds on the specific volume also applies to the Navier-Stokes equations. The proof relies on a domain decomposition technique and some new dissipative structures to close the nonlinear energy estimates.
Related
- Global weak solutions with vacuum for isentropic compressible Navier-Stokes and Navier-Stokes-Poisson equations in the unit disk under Dirichlet boundary conditions
- Asymptotic behavior of generic Riemann solutions to one-dimensional full compressible Navier-Stokes-Poisson equations
- Time-Decay Rates toward Rarefaction Waves for the One-Dimensional Isentropic Compressible Navier--Stokes Equations
- Global Existence and Large-Time Behavior of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum
- Global Well-Posedness and Large Time Asymptotic Behavior of Strong Solutions to the Compressible Viscous Non-Resistive MHD Equations with Vacuum
BibTeX
@misc{zhang2026large,
title = {{Large time behavior of global solutions to one-dimensional non-isentropic compressible Navier-Stokes-Poisson equations with large initial data}},
author = {Lan Zhang and Huijiang Zhao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06309},
eprint = {2611.06309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06309},
}
RIS
TY - UNPB
TI - Large time behavior of global solutions to one-dimensional non-isentropic compressible Navier-Stokes-Poisson equations with large initial data
AU - Lan Zhang
AU - Huijiang Zhao
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06309
UR - https://arxiv.org/abs/2611.06309
AB - In this paper, we are concerned with the construction of global solutions to the Cauchy problem for the one-dimensional non-isentropic compressible Navier-Stokes-Poisson equations, as well as the precise description of their large-time behavior. While results for small initial data are well-established, the case of large initial perturbations remains less satisfactory. Even for constant transport coefficients, only the Nishida-Smoller type solutions have been obtained so far. In this work, we will provide a complete resolution of this problem. The key idea involves revealing favorable hidden identities of the potential force and a new representation for the specific volume, which enables us to derive uniform upper and lower bounds on this quantity. Moreover, this strategy extends to compressible viscous single-ion flow under the Boltzmann relation; notably, this new method for deriving lower and upper bounds on the specific volume also applies to the Navier-Stokes equations. The proof relies on a domain decomposition technique and some new dissipative structures to close the nonlinear energy estimates.
ER -