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

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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.

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Acknowledgements

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.

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  1. Department of Mathematics, Yonsei University, Seoul, Republic of Korea

    Kyungkeun Kang

  2. Department of Mathematics Education, Hannam University, Daejeon, Republic of Korea

    Hwa Kil Kim

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  1. Kyungkeun Kang
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Correspondence to Hwa Kil Kim.

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Kang, K., Kim, H.K. Local well-posedness in the Wasserstein space for a chemotaxis model coupled to incompressible fluid flows. Z. Angew. Math. Phys. 73, 138 (2022). https://doi.org/10.1007/s00033-022-01778-w

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  • DOI: https://doi.org/10.1007/s00033-022-01778-w

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