Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations

Hantaek Bae; Kyungkeun Kang; Seick Kim

doi:10.1016/j.jde.2018.01.007

Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations

Hantaek Bae, Kyungkeun Kang, Seick Kim

Department of Mathematics

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

Abstract

We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller–Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.

Original language	English
Pages (from-to)	5360-5387
Number of pages	28
Journal	Journal of Differential Equations
Volume	264
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2018.01.007
Publication status	Published - 2018 Apr 15

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2018.01.007

Cite this

@article{f9152b0784d84146ab0f7b8ef03e6231,

title = "Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations",

abstract = "We prove the uniqueness of H{\"o}lder continuous weak solutions via duality argument and vanishing viscosity method for the Keller–Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.",

keywords = "Duality argument, Green matrix of parabolic equation, Keller–Segel equation, Porous media, Uniqueness, Vanishing viscosity",

author = "Hantaek Bae and Kyungkeun Kang and Seick Kim",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = apr,

day = "15",

doi = "10.1016/j.jde.2018.01.007",

language = "English",

volume = "264",

pages = "5360--5387",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "8",

}

TY - JOUR

T1 - Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations

AU - Bae, Hantaek

AU - Kang, Kyungkeun

AU - Kim, Seick

PY - 2018/4/15

Y1 - 2018/4/15

N2 - We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller–Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.

AB - We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller–Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.

KW - Duality argument

KW - Green matrix of parabolic equation

KW - Keller–Segel equation

KW - Porous media

KW - Uniqueness

KW - Vanishing viscosity

UR - http://www.scopus.com/inward/record.url?scp=85039940340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039940340&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2018.01.007

DO - 10.1016/j.jde.2018.01.007

M3 - Article

AN - SCOPUS:85039940340

SN - 0022-0396

VL - 264

SP - 5360

EP - 5387

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 8

ER -

Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this