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

摘要

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.