Global existence and boundedness of classical solutions in chemotaxis-(Navier-)Stokes system with singular sensitivity and self-consistent term

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Yuying Wang, Liqiong Pu, Jiashan Zheng
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It is confirmed that for any selection of <span><math><mi>χ</mi></math></span> satisfying <span><span><span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>χ</mi><mo>≤</mo><mfrac><mrow><msqrt><mrow><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><msubsup><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mo>ln</mo></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><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><mo>)</mo></mrow><mo>+</mo><mi>k</mi><msup><mrow><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>ln</mo></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><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><mo>)</mo></mrow><mo>)</mo></mrow></mrow></msqrt><mo>−</mo><mi>k</mi><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>ln</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><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><mo>)</mo></mrow></mrow><mrow><mi>k</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>ln</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><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><mo>)</mo></mrow></mrow></mfrac></mrow></math></span></span></span>with <span><math><mrow><mi>k</mi><mo>→</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span> and <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>→</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></math></span>, then the corresponding problem <span><span>(*)</span></span> admits a globally and uniformly bounded classical solution via an approach to introduce a trigonometric-type weight function.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109518"},"PeriodicalIF":2.9000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925000680","RegionNum":2,"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

This paper addresses the global existence and boundedness of classical solutions to the Neumann-Neumann-Dirichlet value problem for the chemotaxis system, as described by (*)nt+un=Δnχn1+cc+(nϕ),xΩ,t>0,ct+uc=Δcnαc,xΩ,t>0,ut+P=Δunϕ+n1+cc,xΩ,t>0,u=0,xΩ,t>0nν=cν=0,u=0,xΩ,t>0n(x,0)=n0(x),c(x,0)=c0(x),u(x,0)=u0(x),xΩin a smoothly bounded domain ΩRN(N=2,3), where α>0 and the gravitational potential function ϕW1,(Ω). It is confirmed that for any selection of χ satisfying 0<χk2δ12ln2(1+c0L(Ω))+k(k1)2(π2+ln2(1+c0L(Ω)))kδ1ln(1+c0L(Ω))k(k1)ln(1+c0L(Ω))with kN2 and δ1k1, then the corresponding problem (*) admits a globally and uniformly bounded classical solution via an approach to introduce a trigonometric-type weight function.
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来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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