Communications in Mathematical Physics

, Volume 359, Issue 3, pp 951–973 | Cite as

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Interdisciplinary Graduate School of Science and TechnologyShinshu UniversityMatsumotoJapan
  2. 2.Department of Mathematical SciencesShinshu UniversityMatsumotoJapan

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