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Brezis–Gallouet–Wainger Type Inequalities and Blow-Up Criteria for Navier–Stokes Equations in Unbounded Domains

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Abstract

We shall find the weakest norm that satisfies the Brezis–Gallouet–Wainger type inequality, under some conditions. As an application of the Brezis–Gallouet–Wainger type inequality, we shall establish Beale–Kato–Majda type blow-up criteria of smooth solutions to the 3-D Navier–Stokes equations in unbounded domains.

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Authors and Affiliations

  1. Interdisciplinary Graduate School of Science and Technology, Shinshu University, Matsumoto, 390-8621, Japan

    Kohei Nakao

  2. Department of Mathematical Sciences, Shinshu University, Matsumoto, 390-8621, Japan

    Yasushi Taniuchi

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  1. Kohei Nakao
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  2. Yasushi Taniuchi
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Correspondence to Yasushi Taniuchi.

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Communicated by W. Schlag

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Nakao, K., Taniuchi, Y. Brezis–Gallouet–Wainger Type Inequalities and Blow-Up Criteria for Navier–Stokes Equations in Unbounded Domains. Commun. Math. Phys. 359, 951–973 (2018). https://doi.org/10.1007/s00220-017-3061-0

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  • DOI: https://doi.org/10.1007/s00220-017-3061-0

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