Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup>
In this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semanti...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-03-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/3/171 |
| _version_ | 1827307114514612224 |
|---|---|
| author | Yuting Xu Qianfan Liu Yao Chen Yang Lei Minghua Yang |
| author_facet | Yuting Xu Qianfan Liu Yao Chen Yang Lei Minghua Yang |
| author_sort | Yuting Xu |
| collection | DOAJ |
| description | In this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>χ</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>ξ</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>λ</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>. The system is a model that involves double chemosignals; one is an attractant consumed by the cells themselves, and the other is an attractant or a repellent produced by the cells themselves. We prove the global-in-time existence and uniqueness of the weak solution to the system for a large class of initial data on the whole space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula>. |
| first_indexed | 2024-04-24T18:33:47Z |
| format | Article |
| id | doaj.art-cf4ae1b4ff5941df831f4601358aaee9 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-04-24T18:33:47Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-cf4ae1b4ff5941df831f4601358aaee92024-03-27T13:21:01ZengMDPI AGAxioms2075-16802024-03-0113317110.3390/axioms13030171Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup>Yuting Xu0Qianfan Liu1Yao Chen2Yang Lei3Minghua Yang4Department of Mathematics, Nanchang Normal University, Nanchang 330029, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang 330032, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang 330032, ChinaDepartment of Mathematics, Jiangxi University of Finance and Economics, Nanchang 330032, ChinaDepartment of Mathematics, Jiangxi University of Finance and Economics, Nanchang 330032, ChinaIn this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>χ</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>ξ</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>λ</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>. The system is a model that involves double chemosignals; one is an attractant consumed by the cells themselves, and the other is an attractant or a repellent produced by the cells themselves. We prove the global-in-time existence and uniqueness of the weak solution to the system for a large class of initial data on the whole space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula>.https://www.mdpi.com/2075-1680/13/3/171chemotaxisattractionrepulsionNavier–Stokesweak solutionslogistic source |
| spellingShingle | Yuting Xu Qianfan Liu Yao Chen Yang Lei Minghua Yang Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup> Axioms chemotaxis attraction repulsion Navier–Stokes weak solutions logistic source |
| title | Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup> |
| title_full | Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup> |
| title_fullStr | Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup> |
| title_full_unstemmed | Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup> |
| title_short | Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup>2</sup> |
| title_sort | global existence of chemotaxis navier stokes system with logistic source on the whole space inline formula math display inline semantics mrow mi mathvariant double struck r mi mrow semantics math inline formula sup 2 sup |
| topic | chemotaxis attraction repulsion Navier–Stokes weak solutions logistic source |
| url | https://www.mdpi.com/2075-1680/13/3/171 |
| work_keys_str_mv | AT yutingxu globalexistenceofchemotaxisnavierstokessystemwithlogisticsourceonthewholespaceinlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasup2sup AT qianfanliu globalexistenceofchemotaxisnavierstokessystemwithlogisticsourceonthewholespaceinlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasup2sup AT yaochen globalexistenceofchemotaxisnavierstokessystemwithlogisticsourceonthewholespaceinlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasup2sup AT yanglei globalexistenceofchemotaxisnavierstokessystemwithlogisticsourceonthewholespaceinlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasup2sup AT minghuayang globalexistenceofchemotaxisnavierstokessystemwithlogisticsourceonthewholespaceinlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasup2sup |