The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations

Youngwoo Koh; Minsuk Yang

The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations

Analysis of PDEs 2016-05-17 v2

Authors: Youngwoo Koh , Minsuk Yang

Abstract

We study the possible interior singular points of suitable weak solutions to the three dimensional incompressible Navier--Stokes equations. We present an improved parabolic upper Minkowski dimension of the possible singular set. It is bounded by $95/63$ . The result also continue to hold for the three dimensional incompressible magnetohydrodynamic equations without any difficulty.

Keywords

incompressible Navier-Stokes equations interior singular points Minkowski dimension suitable weak solutions singular set magnetohydrodynamic equations upper bound

Cite

@article{arxiv.1603.01007,
  title  = {The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations},
  author = {Youngwoo Koh and Minsuk Yang},
  journal= {arXiv preprint arXiv:1603.01007},
  year   = {2016}
}

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