{"title":"粘性接触波对一维可压缩纳维-斯托克斯方程的稳定性和衰减率","authors":"Xinxiang Bian, Lingling Xie","doi":"10.4310/cms.2024.v22.n2.a2","DOIUrl":null,"url":null,"abstract":"This paper studies the large-time asymptotic stability and optimal time-decay rate of viscous contact wave to one-dimensional compressible Navier–Stokes equations. We prove that one-dimensional compressible Navier–Stokes equations are asymptotically stable for viscous contact wave with arbitrarily large strength, under large initial perturbations. The time optimal decay rate of viscous contact wave is also obtained under the small initial perturbations. In the proof, the Lagrange transform is used to cancel the convection terms, which are difficult to estimate due to the lower spatial derivatives compared with the diffusion terms.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"71 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability and decay rate of viscous contact wave to one-dimensional compressible Navier-Stokes equations\",\"authors\":\"Xinxiang Bian, Lingling Xie\",\"doi\":\"10.4310/cms.2024.v22.n2.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the large-time asymptotic stability and optimal time-decay rate of viscous contact wave to one-dimensional compressible Navier–Stokes equations. We prove that one-dimensional compressible Navier–Stokes equations are asymptotically stable for viscous contact wave with arbitrarily large strength, under large initial perturbations. The time optimal decay rate of viscous contact wave is also obtained under the small initial perturbations. In the proof, the Lagrange transform is used to cancel the convection terms, which are difficult to estimate due to the lower spatial derivatives compared with the diffusion terms.\",\"PeriodicalId\":50659,\"journal\":{\"name\":\"Communications in Mathematical Sciences\",\"volume\":\"71 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cms.2024.v22.n2.a2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n2.a2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Stability and decay rate of viscous contact wave to one-dimensional compressible Navier-Stokes equations
This paper studies the large-time asymptotic stability and optimal time-decay rate of viscous contact wave to one-dimensional compressible Navier–Stokes equations. We prove that one-dimensional compressible Navier–Stokes equations are asymptotically stable for viscous contact wave with arbitrarily large strength, under large initial perturbations. The time optimal decay rate of viscous contact wave is also obtained under the small initial perturbations. In the proof, the Lagrange transform is used to cancel the convection terms, which are difficult to estimate due to the lower spatial derivatives compared with the diffusion terms.
期刊介绍:
Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.