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

Funding Information:
S. Kim was supported by NRF-20151009350.

Funding Information:
H. Bae was supported by NRF-2015R1D1A1A01058892.

Funding Information:
K. Kang was supported by NRF-2017R1A2B4006484 and NRF-20151009350.

Publisher Copyright:
© 2018 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2018.01.007

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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.",

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

note = "Funding Information: S. Kim was supported by NRF-20151009350. Funding Information: H. Bae was supported by NRF-2015R1D1A1A01058892. Funding Information: K. Kang was supported by NRF-2017R1A2B4006484 and NRF-20151009350. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = apr,

day = "15",

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

language = "English",

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journal = "Journal of Differential Equations",

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AU - Bae, Hantaek

AU - Kang, Kyungkeun

AU - Kim, Seick

N1 - Funding Information: S. Kim was supported by NRF-20151009350. Funding Information: H. Bae was supported by NRF-2015R1D1A1A01058892. Funding Information: K. Kang was supported by NRF-2017R1A2B4006484 and NRF-20151009350. Publisher Copyright: © 2018 Elsevier Inc.

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.

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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

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