On the possible time singularities for the 3D Navier-Stokes equations

Abstract

We prove a local-in-time regularity criterion for the 3D Navier-Stokes equations. In particular, it follows from the criterion that the Hausdorff dimension of possible singular times of Leray-Hopf weak solutions $u\in L_t^r{B}_{s,\infty }^{\alpha }$ for some $\alpha >0$, $s>3$ and $r>2$ is less than $\frac{r}{2}(\frac{3}{s}+\frac{2}{r}-\alpha -1)$. The main contribution is that we do not assume the suitability of weak solutions.

11 pages; v4 includes a wider range of spaces

References in corpus (1)

• Weak in Space, Log in Time Improvement of the Lady{ž}enskaja-Prodi-Serrin Criteria