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Research Article | Open Access

Existence of generalized solutions for Keller-Segel-Navier-Stokes equations with degradation in dimension three

Kyungkeun Kang( ), Dongkwang Kim
School of Mathematics & Computing(Mathematics), Yonsei University, Seoul 03722, Republic of Korea
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Abstract

We construct generalized solutions for the Keller-Segel system with a degradation source coupled to Navier Stokes equations in three dimensions, in case that the power of degradation is smaller than quadratic. Furthermore, if the logistic type source is purely damping with no growing effect, we prove that solutions converge to zero in some norms and provide upper bounds of convergence rates in time.

Keywords

chemotaxisgeneralized solutionKeller-Segel-Navier-Stokes equationsasymptotic behavior

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Mathematics in Engineering
Volume 4 Issue 5,
October 2022
Pages 1-25
DOI: 10.3934/mine.2022041

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Cite this article:
Kang K, Kim D. Existence of generalized solutions for Keller-Segel-Navier-Stokes equations with degradation in dimension three. Mathematics in Engineering, 2022, 4(5): 1-25. https://doi.org/10.3934/mine.2022041

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Received: 31 December 2020
Accepted: 06 July 2021
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)