### Abstract

We consider a coupled system of Keller-Segel-type equations and the incompressible Navier-Stokes equations in spatial dimension two and three. We first establish the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space under the assumption that initial mass is integrable and has finite entropy. As a result, we construct 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 the case that its initial mass is assumed to be bounded and integrable.

Original language | English |
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Pages (from-to) | 2965-3004 |

Number of pages | 40 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 49 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*49*(4), 2965-3004. https://doi.org/10.1137/16M1083232

}

*SIAM Journal on Mathematical Analysis*, vol. 49, no. 4, pp. 2965-3004. https://doi.org/10.1137/16M1083232

**Existence of weak solutions in wasserstein space for a chemotaxis model coupled to fluid equations.** / Kang, Kyungkeun; Kim, Hwa Kil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Existence of weak solutions in wasserstein space for a chemotaxis model coupled to fluid equations

AU - Kang, Kyungkeun

AU - Kim, Hwa Kil

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We consider a coupled system of Keller-Segel-type equations and the incompressible Navier-Stokes equations in spatial dimension two and three. We first establish the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space under the assumption that initial mass is integrable and has finite entropy. As a result, we construct 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 the case that its initial mass is assumed to be bounded and integrable.

AB - We consider a coupled system of Keller-Segel-type equations and the incompressible Navier-Stokes equations in spatial dimension two and three. We first establish the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space under the assumption that initial mass is integrable and has finite entropy. As a result, we construct 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 the case that its initial mass is assumed to be bounded and integrable.

UR - http://www.scopus.com/inward/record.url?scp=85028621167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028621167&partnerID=8YFLogxK

U2 - 10.1137/16M1083232

DO - 10.1137/16M1083232

M3 - Article

AN - SCOPUS:85028621167

VL - 49

SP - 2965

EP - 3004

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 4

ER -