CSIAM Trans. Appl. Math., 6 (2025), pp. 799-841.
Published online: 2025-09
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This paper is concerned with a two-species Keller-Segel-Navier-Stokes model with sub-logistic source in a bounded domain with smooth boundary under noflux/no-flux/no-flux/Dirichlet boundary conditions. For a large class of cell kinetics including sub-logistic degradation, it is shown that under an explicit condition involving the chemotactic strength and initial mass of cells, the two-dimensional Keller-Segel-Navier-Stokes problem possesses a global and bounded classical solution. In the case with arbitrary superlinear logistic degradation, it is proved that for all suitably regular initial data, the two-dimensional Keller-Segel-Navier-Stokes problem has at least one globally defined solution in an appropriate generalized sense. These results improves and extends the previously known ones.
}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2024-0016}, url = {http://global-sci.org/intro/article_detail/csiam-am/24503.html} }This paper is concerned with a two-species Keller-Segel-Navier-Stokes model with sub-logistic source in a bounded domain with smooth boundary under noflux/no-flux/no-flux/Dirichlet boundary conditions. For a large class of cell kinetics including sub-logistic degradation, it is shown that under an explicit condition involving the chemotactic strength and initial mass of cells, the two-dimensional Keller-Segel-Navier-Stokes problem possesses a global and bounded classical solution. In the case with arbitrary superlinear logistic degradation, it is proved that for all suitably regular initial data, the two-dimensional Keller-Segel-Navier-Stokes problem has at least one globally defined solution in an appropriate generalized sense. These results improves and extends the previously known ones.