Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

Myeongju Chae; Kyungkeun Kang; Jihoon Lee

doi:10.1080/03605302.2013.852224

Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

Myeongju Chae, Kyungkeun Kang, Jihoon Lee

Department of Mathematics

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

112 Citations (Scopus)

Abstract

We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.

Original language	English
Pages (from-to)	1205-1235
Number of pages	31
Journal	Communications in Partial Differential Equations
Volume	39
Issue number	7
DOIs	https://doi.org/10.1080/03605302.2013.852224
Publication status	Published - 2014 Jul

Bibliographical note

Funding Information:
M. Chae’s work was partially supported by NRF-2011-0028951. K. Kang’s work was partially supported by NRF-2012R1A1A2001373. J. Lee’s work was partially supported by NRF-2011-0006697 and Chung-Ang University Research Grants in 2013.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/03605302.2013.852224

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abstract = "We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.",

author = "Myeongju Chae and Kyungkeun Kang and Jihoon Lee",

note = "Funding Information: M. Chae{\textquoteright}s work was partially supported by NRF-2011-0028951. K. Kang{\textquoteright}s work was partially supported by NRF-2012R1A1A2001373. J. Lee{\textquoteright}s work was partially supported by NRF-2011-0006697 and Chung-Ang University Research Grants in 2013.",

year = "2014",

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AU - Chae, Myeongju

AU - Kang, Kyungkeun

AU - Lee, Jihoon

N1 - Funding Information: M. Chae’s work was partially supported by NRF-2011-0028951. K. Kang’s work was partially supported by NRF-2012R1A1A2001373. J. Lee’s work was partially supported by NRF-2011-0006697 and Chung-Ang University Research Grants in 2013.

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N2 - We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.

AB - We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.

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Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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