{"title":"On the Weak Solutions to the Multicomponent Reactive Flows Driven by Non-conservative Boundary Conditions","authors":"Bingkang Huang","doi":"10.1007/s00021-024-00856-5","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a new concept of weak solutions to the multicomponent reactive flows driven by large boundary data. When the Gibbs’ equation incorporates the species mass fractions, we establish the global-in-time existence of weak solutions for any finite energy initial data. Moreover, if the classical solutions exist, the weak solutions coincide with them in the same time interval.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00856-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a new concept of weak solutions to the multicomponent reactive flows driven by large boundary data. When the Gibbs’ equation incorporates the species mass fractions, we establish the global-in-time existence of weak solutions for any finite energy initial data. Moreover, if the classical solutions exist, the weak solutions coincide with them in the same time interval.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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