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The Navier–Stokes equations with the Neumann boundary condition in an infinite cylinder

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Abstract

We prove unique existence of local-in-time smooth solutions of the Navier–Stokes equations for initial data in \(L^{p}\) and \(p\in [3,\infty )\) in an infinite cylinder, subject to the Neumann boundary condition.

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Acknowledgements

The author is partially supported by JSPS through the Grant-in-aid for Young Scientist (B) 17K14217, Scientific Research (B) 17H02853 and Osaka City University Strategic Research Grant 2018 for young researchers.

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  1. Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    K. Abe

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Abe, K. The Navier–Stokes equations with the Neumann boundary condition in an infinite cylinder. manuscripta math. 160, 359–383 (2019). https://doi.org/10.1007/s00229-018-01102-9

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