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arXiv · 1604.05032

On the box-counting dimension of potential singular set for suitable weak solutions to the 3D Navier-Stokes equations

Yanqing Wang·Gang Wu
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Abstract

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 taking full advantage of the pressure $\Pi$ in terms of $\nabla \Pi$ in equations, we show that this upper box dimension is at most $135/104(\approx1.30)$, which improves the known upper box-counting dimension $95/63(\approx1.51)$ in Koh et al. [9, J. Differential Equations, 261: 3137--3148, 2016], $45/29(\approx1.55)$ in Kukavica et al. [11, Nonlinearity 25: 2775-2783, 2012] and $135/82(\approx1.65)$ in Kukavica [10, Nonlinearity 22: 2889-2900, 2009].

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Yanqing Wang, Gang Wu. 2016-04-18. On the box-counting dimension of potential singular set for suitable weak solutions to the 3D Navier-Stokes equations. https://doi.org/10.1088/1361-6544/aa6444

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