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

Kyungkeun Kang; Dongkwang Kim

doi:10.3934/MINE.2022041

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

Kyungkeun Kang, Dongkwang Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Journal	Mathematics In Engineering
Volume	4
Issue number	5
DOIs	https://doi.org/10.3934/MINE.2022041
Publication status	Published - 2022

Bibliographical note

Funding Information:
K. Kang is partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. Kim is supported by NRF-2019R1A2C1084685.

Publisher Copyright:
© 2022 the Author(s),

All Science Journal Classification (ASJC) codes

Applied Mathematics
Mathematical Physics
Analysis

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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.",

author = "Kyungkeun Kang and Dongkwang Kim",

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AU - Kim, Dongkwang

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

Abstract

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