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A Note on the Regularity Time of Leray Solutions to the Navier–Stokes Equations

  • P. Braz e SilvaEmail author
  • J. P. Zingano
  • P. R. Zingano
Article
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Abstract

In this note we slightly improve a well known result about the regularity time of Leray solutions \({{\varvec{u}}}(\cdot ,t)\) to the Navier–Stokes equations in \( \mathbb {R}^{n} \!\,\!\) (\(n \le 4\)). A related result on the eventual monotonicity of \( \,\! \Vert \;\!D^{m}{{\varvec{u}}}(\cdot ,t) \,\!\Vert _{L^{2}(\mathbb {R}^{n})} \!\;\!\) for arbitrary \( m \,\!\) is also discussed.

Notes

Acknowledgements

Funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant No. 309491/2015-0). P. Braz e Silva was funded by this grant.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departmento de MatemáticaUniversidade Federal de PernambucoRecifeBrazil
  2. 2.Departamento de Matemática Pura e AplicadaUniversidade Federal do Rio Grande do SulPorto AlegreBrazil

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