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

118 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

Access to Document

10.1080/03605302.2013.852224

Cite this

@article{6c575f54974f4787b260860f8b133fd6,

title = "Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations",

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",

month = jul,

doi = "10.1080/03605302.2013.852224",

language = "English",

volume = "39",

pages = "1205--1235",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "7",

}

TY - JOUR

T1 - Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

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.

PY - 2014/7

Y1 - 2014/7

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.

UR - http://www.scopus.com/inward/record.url?scp=84901273571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901273571&partnerID=8YFLogxK

U2 - 10.1080/03605302.2013.852224

DO - 10.1080/03605302.2013.852224

M3 - Article

AN - SCOPUS:84901273571

VL - 39

SP - 1205

EP - 1235

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 7

ER -

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this