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

Kyungkeun Kang; Dongkwang Kim; Kyungkeun Kang; Dongkwang Kim

doi:10.3934/mine.2022041

Mathematics in Engineering

2022, Volume 4, Issue 5: 1-25. doi: 10.3934/mine.2022041

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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

Received: 31 December 2020 Accepted: 06 July 2021 Published: 12 October 2021

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.
- chemotaxis,
- generalized solution,
- Keller-Segel-Navier-Stokes equations,
- asymptotic behavior
Citation: Kyungkeun Kang, Dongkwang Kim. Existence of generalized solutions for Keller-Segel-Navier-Stokes equations with degradation in dimension three[J]. Mathematics in Engineering, 2022, 4(5): 1-25. doi: 10.3934/mine.2022041

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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.

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