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, Volume 160, Issue 3–4, pp 359–383 | Cite as

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.

Mathematics Subject Classification

35Q35 35K90 

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Notes

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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceOsaka City UniversityOsakaJapan

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