Global relaxation limit for the one-fluid Euler-Poisson system with large smooth data

Mathematics > Analysis of PDEs [Submitted on 16 Jun 2026] Title:Global relaxation limit for the one-fluid Euler-Poisson system with large smooth data View PDF HTML (experimental)Abstract:Whether the multi-dimensional Euler-Poisson system admits global smooth solutions remains a challenging open problem. In this paper, we construct a class of large-data global smooth solutions to the one-fluid Euler-Poisson system in $\mathbb{R}^d$ ($1\leq d\leq 5$) by using the relaxation dissipation mechanism. Precisely, assuming that the initial density is far from vacuum and $\varepsilon E_0$ is sufficiently small, where $E_0$ denotes the initial energy and $\varepsilon$ is the relaxation time, we establish the global well-posedness of smooth solutions to the Cauchy problem. In particular, the size of the initial perturbation may be arbitrarily large, provided that the relaxation time is sufficiently small. Furthermore, we introduce an effective unknown motivated by Darcy's law to derive quantitative error estimates at the rate $\mathcal O(e^{-\lambda t}\varepsilon)$ between the rescaled Euler-Poisson system and the limiting drift-diffusion system for ill-prepared data. The new ingredient lies in developing the maximum principle for the nonlinear drift-diffusion system with nonlocal effect, which leads to the large-data global existence. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.