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



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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© 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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