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Advances in the 3D Navier-Stokes Equations

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Qualitative and Quantitative Analysis of Nonlinear Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 111))

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Abstract

In this chapter we provide a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data. Moreover, we establish sufficient conditions for Leray-Hopf property of a weak solution for the 3D Navier-Stokes system. Under such conditions this weak solution is rightly continuous in the standard phase space H endowed with the strong convergence topology.

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Authors and Affiliations

  1. Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

    Michael Z. Zgurovsky

  2. Institute for Applied System Analysis, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

    Pavlo O. Kasyanov

Authors
  1. Michael Z. Zgurovsky
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  2. Pavlo O. Kasyanov
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Correspondence to Michael Z. Zgurovsky .

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Zgurovsky, M.Z., Kasyanov, P.O. (2018). Advances in the 3D Navier-Stokes Equations. In: Qualitative and Quantitative Analysis of Nonlinear Systems. Studies in Systems, Decision and Control, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-59840-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-59840-6_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59839-0

  • Online ISBN: 978-3-319-59840-6

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