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Anisotropic and Geometric Criteria for Interior Regularity of Weak Solutions to the 3D Navier—Stokes Equations

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Mathematical Fluid Mechanics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

We formulate sufficient conditions for regularity of a suitable weak solution(v; p ) in a sub—domainD of the time—space cylinderQT in Section 3. The conditions are anisotropic in the sense that the assumptions about vi v2 (the first two components of velocity) differ from the assumptions about the third component of velocity v3. The question what types of deformations of infinitely small volumes of the fluid support regularity and what types contribute to a blow—up is studied in Section 4. Finally, we mention some open problems in Section 5.

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Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35, Praha 2, Czech Republic

    Jiří Neustupa

  2. Université de Toulon et du Var, Mathématique, 83957, La Garde, France

    Patrick Penel

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  1. Jiří Neustupa
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  2. Patrick Penel
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Editors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Karlovo nám. 13, 121 35, Praha 2, Czech Republic

    Jiří Neustupa

  2. Département de Mathématiques, Université de Toulon et du Var, B.P. 132, 83957, La Garde Cedex, France

    Patrick Penel

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Neustupa, J., Penel, P. (2001). Anisotropic and Geometric Criteria for Interior Regularity of Weak Solutions to the 3D Navier—Stokes Equations. In: Neustupa, J., Penel, P. (eds) Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8243-9_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8243-9_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9489-0

  • Online ISBN: 978-3-0348-8243-9

  • eBook Packages: Springer Book Archive

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