{"title":"Wave propagation for the isentropic compressible Navier–Stokes/Allen–Cahn system","authors":"Yazhou Chen, Houzhi Tang, Yue Zhang","doi":"10.1002/mma.10458","DOIUrl":null,"url":null,"abstract":"<p>We study the Cauchy problem for the three-dimensional isentropic compressible Navier–Stokes/Allen–Cahn system, which models the phase transitions in two-component patterns interacting with a compressible fluid. Under the assumption that the initial perturbation is small and decays spatially, we establish the global existence and the pointwise behavior of strong solutions to this nonconserved system. To deal with the source terms involving the phase variable, we employ the Green's function and space-time weighted estimates. The analysis shows that the phase variable mainly contains the diffusion wave with exponential decaying amplitude over time, and consequently the density and momentum of the compressible fluid adhere to a generalized Huygens principle.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"2726-2742"},"PeriodicalIF":1.8000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10458","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
We study the Cauchy problem for the three-dimensional isentropic compressible Navier–Stokes/Allen–Cahn system, which models the phase transitions in two-component patterns interacting with a compressible fluid. Under the assumption that the initial perturbation is small and decays spatially, we establish the global existence and the pointwise behavior of strong solutions to this nonconserved system. To deal with the source terms involving the phase variable, we employ the Green's function and space-time weighted estimates. The analysis shows that the phase variable mainly contains the diffusion wave with exponential decaying amplitude over time, and consequently the density and momentum of the compressible fluid adhere to a generalized Huygens principle.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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