Improved bounds for box dimensions of potential singular points to the Navier–Stokes equations

Yanqing Wang, Minsuk Yang

Type: Article

Publication Date: 2019-10-29

Citations: 5

DOI: https://doi.org/10.1088/1361-6544/ab3f51

Abstract

In this paper, we study the potential singular points of interior and boundary suitable weak solutions to the 3D Navier--Stokes equations. It is shown that upper box dimension of interior singular points and boundary singular points are bounded by $7/6$ and $10/9$, respectively. Both proofs rely on recent progress of $\varepsilon$-regularity criteria at one scale.

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+	On Partial Regularity of Suitable Weak Solutions to the Three-Dimensional NavierStokes equations	1999	O. A. Ladyzhenskaya G. Serëgin
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+	Local Regularity of Suitable Weak Solutions to the Navier--Stokes Equations Near the Boundary	2002	G. Serëgin
+	Partial regularity of suitable weak solutions of the navier‐stokes equations	1982	Luis Caffarelli Robert V. Kohn Louis Nirenberg
+ PDF Chat	Fractal Geometry: Mathematical Foundations and Applications.	1990	K. J. Falconer
+	A new proof of partial regularity of solutions to Navier-Stokes equations	2007	Alexis Vasseur
+ PDF Chat	A solution to the Navier-Stokes inequality with an internal singularity	1985	Vladimir Scheffer
+	Abstract Lp estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains	1991	Yoshikazu Giga Hermann Sohr
+	A new proof of the Caffarelli-Kohn-Nirenberg theorem	1998	Fanghua Lin