A ε-regularity criterion without pressure of suitable weak solutions to the Navier-Stokes equations at one scale

2018/11/25 by Wang, Yanqing, Wu, Gang, Zhou, Daoguo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.09927

Abstract

In this paper, we continue our work in [15] to derive ε-regularity criteria at one scale without pressure for suitable weak solutions to the Navier-Stokes equations. We establish a ε-regularity criterion below of suitable weak solutions, for any δ>0, \iint_Q(1)|u|^(5)/(2)+δdxdt≤ ε. As an application, we extend the previous corresponding results concerning the improvement of the classical Caffarelli--Kohn--Nirenberg theorem by a logarithmic factor.

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