Communications in Mathematical Sciences
Volume 11 (2013)
A remark on the box-counting dimension of the singular set for the Navier–Stokes equations
Pages: 597 – 602
Let $u$ be a suitable weak solution of the Navier–Stokes equations and let $S$ be the set of its singular points in space-time. We prove that if $u_t$ is square integrable then the box-counting dimension of $S$ is no larger than one.
Navier–Stokes equations, singular set, partial regularity, box-counting dimension
2010 Mathematics Subject Classification
35K55, 35Q30, 35Q35