A regularity condition and temporal asymptotics for chemotaxis-fluid equations

Myeongju Chae; Kyungkeun Kang; Jihoon Lee; Ki Ahm Lee

doi:10.1088/1361-6544/aa92ec

A regularity condition and temporal asymptotics for chemotaxis-fluid equations

Myeongju Chae, Kyungkeun Kang, Jihoon Lee, Ki Ahm Lee

Department of Mathematics

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

9 Citations (Scopus)

Abstract

We consider two dimensional chemotaxis equations coupled to the Navier-Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae et al (2013 Discrete Continuous Dyn. Syst. A 33 2271-97) and Chae et al (2014 Commun.

Original language	English
Article number	351
Journal	Nonlinearity
Volume	31
Issue number	2
DOIs	https://doi.org/10.1088/1361-6544/aa92ec
Publication status	Published - 2018 Jan 3

Bibliographical note

Funding Information:
M Chae was supported by NRF-2015R1C1A2A01054919. K Kang was supported by NRF-2014R1A2A1A11051161. J Lee was supported by NRF-2016R1A2B3011647. Ki-Ahm Lee was supported by NRF-2015R1A4A1041675. Ki-Ahm Lee also hold a joint appointment with the Research Institute of Mathematics of Seoul National University.

Publisher Copyright:
© 2018 IOP Publishing Ltd & London Mathematical Society.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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Cite this

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abstract = "We consider two dimensional chemotaxis equations coupled to the Navier-Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae et al (2013 Discrete Continuous Dyn. Syst. A 33 2271-97) and Chae et al (2014 Commun.",

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AU - Chae, Myeongju

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Y1 - 2018/1/3

N2 - We consider two dimensional chemotaxis equations coupled to the Navier-Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae et al (2013 Discrete Continuous Dyn. Syst. A 33 2271-97) and Chae et al (2014 Commun.

AB - We consider two dimensional chemotaxis equations coupled to the Navier-Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae et al (2013 Discrete Continuous Dyn. Syst. A 33 2271-97) and Chae et al (2014 Commun.

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A regularity condition and temporal asymptotics for chemotaxis-fluid equations

Abstract

Bibliographical note

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