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An extension criterion for the local in time solution of the chemotaxis Navier–Stokes equations in the critical Besov spaces

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Abstract

We consider the Keller–Segel model coupled with the incompressible Navier–Stokes equations in the dimension three. Based on the wellposedness result in the critical Besov spaces, we present a result on the extension criterion for the local in time solution in the same functional setting, which is a new result for the model.

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Acknowledgments

We express our sincere gratitude for very helpful and constructive comments of the reviewer. This work was supported by NRF under the grant 20151002708.

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Authors and Affiliations

  1. Mathematics Department, Yonsei university, Seoul, South Korea

    Hi Jun Choe

  2. Mathematics Department, Chosun university, Gwangju, South Korea

    Bataa Lkhagvasuren

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  1. Hi Jun Choe
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  2. Bataa Lkhagvasuren
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Correspondence to Bataa Lkhagvasuren.

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Choe, H.J., Lkhagvasuren, B. An extension criterion for the local in time solution of the chemotaxis Navier–Stokes equations in the critical Besov spaces. Ann Univ Ferrara 63, 277–288 (2017). https://doi.org/10.1007/s11565-016-0265-8

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  • DOI: https://doi.org/10.1007/s11565-016-0265-8

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