Local kinetic energy and singularities of the incompressible Navier--Stokes Equations

2017/05/12 by Choe, Hi Jun, Yang, Minsuk
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.04561

Abstract

We study the partial regularity problem of the incompressible Navier--Stokes equations. In this paper, we show that a reverse Hölder inequality of velocity gradient with increasing support holds under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions v belong to L^∞(0,T;L^3,w(ℝ³)) where L^3,w(ℝ³) denotes the standard weak Lebesgue space.

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