Local well-posedness in the Wasserstein space for a chemotaxis model coupled to incompressible fluid flows

Kyungkeun Kang; Hwa Kil Kim

doi:10.1007/s00033-022-01778-w

Local well-posedness in the Wasserstein space for a chemotaxis model coupled to incompressible fluid flows

Kyungkeun Kang, Hwa Kil Kim

Department of Mathematics

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

Abstract

We consider a coupled system of Keller–Segel-type equations and the incompressible Navier–Stokes equations in spatial dimension two and three. In the previous work [17], we established the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space using the optimal transportation technique. Exploiting this result, we constructed solutions of Keller–Segel–Navier–Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space. In this work, we refine the result on the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space. As a result, we construct solutions of Keller–Segel–Navier–Stokes equations under weaker assumptions on the initial data.

Original language	English
Article number	138
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	73
Issue number	4
DOIs	https://doi.org/10.1007/s00033-022-01778-w
Publication status	Published - 2022 Aug

Bibliographical note

Funding Information:
Kyungkeun Kang’s work is supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. Hwa Kil Kim’s work is supported by NRF-2021R1F1A1048231 and NRF-2018R1D1A1B07049357.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

Access to Document

10.1007/s00033-022-01778-w

Cite this

@article{03badd60ca7a4945bb02688ddb461026,

title = "Local well-posedness in the Wasserstein space for a chemotaxis model coupled to incompressible fluid flows",

abstract = "We consider a coupled system of Keller–Segel-type equations and the incompressible Navier–Stokes equations in spatial dimension two and three. In the previous work [17], we established the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space using the optimal transportation technique. Exploiting this result, we constructed solutions of Keller–Segel–Navier–Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space. In this work, we refine the result on the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space. As a result, we construct solutions of Keller–Segel–Navier–Stokes equations under weaker assumptions on the initial data.",

author = "Kyungkeun Kang and Kim, {Hwa Kil}",

note = "Funding Information: Kyungkeun Kang{\textquoteright}s work is supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. Hwa Kil Kim{\textquoteright}s work is supported by NRF-2021R1F1A1048231 and NRF-2018R1D1A1B07049357. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = aug,

doi = "10.1007/s00033-022-01778-w",

language = "English",

volume = "73",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Local well-posedness in the Wasserstein space for a chemotaxis model coupled to incompressible fluid flows

AU - Kang, Kyungkeun

AU - Kim, Hwa Kil

N1 - Funding Information: Kyungkeun Kang’s work is supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. Hwa Kil Kim’s work is supported by NRF-2021R1F1A1048231 and NRF-2018R1D1A1B07049357. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/8

Y1 - 2022/8

N2 - We consider a coupled system of Keller–Segel-type equations and the incompressible Navier–Stokes equations in spatial dimension two and three. In the previous work [17], we established the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space using the optimal transportation technique. Exploiting this result, we constructed solutions of Keller–Segel–Navier–Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space. In this work, we refine the result on the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space. As a result, we construct solutions of Keller–Segel–Navier–Stokes equations under weaker assumptions on the initial data.

AB - We consider a coupled system of Keller–Segel-type equations and the incompressible Navier–Stokes equations in spatial dimension two and three. In the previous work [17], we established the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space using the optimal transportation technique. Exploiting this result, we constructed solutions of Keller–Segel–Navier–Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space. In this work, we refine the result on the existence of a weak solution of a Fokker–Planck equation in the Wasserstein space. As a result, we construct solutions of Keller–Segel–Navier–Stokes equations under weaker assumptions on the initial data.

UR - http://www.scopus.com/inward/record.url?scp=85133025344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85133025344&partnerID=8YFLogxK

U2 - 10.1007/s00033-022-01778-w

DO - 10.1007/s00033-022-01778-w

M3 - Article

AN - SCOPUS:85133025344

SN - 0044-2275

VL - 73

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 4

M1 - 138

ER -

Local well-posedness in the Wasserstein space for a chemotaxis model coupled to incompressible fluid flows

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this