{"title":"Stability of rarefaction wave for the two-fluid full compressible Navier–Stokes–Poisson system under large initial perturbation","authors":"Qiwei Wu, Xiuli Xu, Jingjun Zhang","doi":"10.1016/j.nonrwa.2025.104380","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we are concerned with the asymptotic behavior of the solution to the Cauchy problem for the one-dimensional two-fluid full (non-isentropic) compressible Navier–Stokes–Poisson system, which models the motion of viscous charged particles (ions and electrons) in plasmas. The rarefaction wave is shown to be time-asymptotically stable under large initial perturbation as long as the strength of the rarefaction wave is sufficiently small and the adiabatic exponent <span><math><mi>γ</mi></math></span> is close to 1. The proof is based on a delicate energy method, and the key point is to derive the uniform bounds of the density functions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104380"},"PeriodicalIF":1.8000,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000665","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we are concerned with the asymptotic behavior of the solution to the Cauchy problem for the one-dimensional two-fluid full (non-isentropic) compressible Navier–Stokes–Poisson system, which models the motion of viscous charged particles (ions and electrons) in plasmas. The rarefaction wave is shown to be time-asymptotically stable under large initial perturbation as long as the strength of the rarefaction wave is sufficiently small and the adiabatic exponent is close to 1. The proof is based on a delicate energy method, and the key point is to derive the uniform bounds of the density functions.
期刊介绍:
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.