{"title":"具有新曼和迪里夏特边界条件的吸引排斥趋化-纳维尔-斯托克斯系统中的全局有界解","authors":"Luli Xu, Chunlai Mu, Minghua Zhang, Jing Zhang","doi":"10.1016/j.nonrwa.2024.104247","DOIUrl":null,"url":null,"abstract":"<div><div>This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> in the explicit expressions for <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> and attraction–repulsion coefficients.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global bounded solution in an attraction repulsion Chemotaxis-Navier-Stokes system with Neumann and Dirichlet boundary conditions\",\"authors\":\"Luli Xu, Chunlai Mu, Minghua Zhang, Jing Zhang\",\"doi\":\"10.1016/j.nonrwa.2024.104247\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> in the explicit expressions for <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> and attraction–repulsion coefficients.</div></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S146812182400186X\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S146812182400186X","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本文讨论了一个吸引-排斥趋化-纳维尔-斯托克斯系统，该系统的吸引信号和排斥信号分别具有迪里夏特边界和诺伊曼边界。在 Winkler (2020) 和 Wang 等人 (2022) 的研究基础上，通过系列估计，证明了在二维中，在‖c0‖L∞(Ω) 和吸引-排斥系数的显式中初始值‖n0‖L1(Ω) 较小的条件下，系统的经典解是全局有界的。
Global bounded solution in an attraction repulsion Chemotaxis-Navier-Stokes system with Neumann and Dirichlet boundary conditions
This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values in the explicit expressions for and attraction–repulsion coefficients.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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