Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion

Yun Sung Chung; Kyungkeun Kang

doi:10.1063/1.4947107

Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion

Yun Sung Chung, Kyungkeun Kang

Department of Mathematics

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

4 Citations (Scopus)

Abstract

We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.

Original language	English
Article number	041503
Journal	Journal of Mathematical Physics
Volume	57
Issue number	4
DOIs	https://doi.org/10.1063/1.4947107
Publication status	Published - 2016 Apr 1

Bibliographical note

Funding Information:
Yun-Sung Chung's work is supported by No. NRF-2012R1A1A2001373 and Kyungkeun Kang's work is supported by No. NRF-2014R1A2A1A11051161 and NRF20151009350.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1063/1.4947107

Fingerprint Dive into the research topics of 'Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion'. Together they form a unique fingerprint.

Cite this

@article{eb7b8e2ccdfb43e2ae345d2f64c9f7b1,

title = "Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion",

abstract = "We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.",

author = "Chung, {Yun Sung} and Kyungkeun Kang",

note = "Funding Information: Yun-Sung Chung's work is supported by No. NRF-2012R1A1A2001373 and Kyungkeun Kang's work is supported by No. NRF-2014R1A2A1A11051161 and NRF20151009350.",

year = "2016",

month = apr,

day = "1",

doi = "10.1063/1.4947107",

language = "English",

volume = "57",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics Publising LLC",

number = "4",

}

TY - JOUR

T1 - Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion

AU - Chung, Yun Sung

AU - Kang, Kyungkeun

N1 - Funding Information: Yun-Sung Chung's work is supported by No. NRF-2012R1A1A2001373 and Kyungkeun Kang's work is supported by No. NRF-2014R1A2A1A11051161 and NRF20151009350.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.

AB - We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.

UR - http://www.scopus.com/inward/record.url?scp=84964915256&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964915256&partnerID=8YFLogxK

U2 - 10.1063/1.4947107

DO - 10.1063/1.4947107

M3 - Article

AN - SCOPUS:84964915256

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

M1 - 041503

ER -