Yanqing Wang, Gang Wu
Published 2016-04-18Version 1
In this paper, we are concerned with the upper box-counting dimension of the set of possible singular points in space-time of suitable weak solutions to the 3D Navier-Stokes equations. By means of the special structure of this system and the interior estimate of harmonic function, we show that this upper box dimension is at most $180/131(\approx1.37)$, which improves the known upper box-counting dimension $95/63(\approx1.51)$ in Koh et al. [7, arXiv: 1603.01007, 2016], $45/29(\approx1.55)$ in Kukavica et al. [9, Nonlinearity 25: 2775-2783, 2012] and $135/82(\approx1.65)$ in Kukavica [8, Nonlinearity 22: 2889-2900, 2009].
New $\varepsilon$-regularity criteria and application to the box dimension of the singular set in the 3D Navier-Stokes equations
Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations
Anisotropic regularity conditions for the suitable weak solutions to the 3d Navier-Stokes equations
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