Dynamics of Partial Differential Equations

Volume 14 (2017)

Number 1

Small $\dot{B}^{-1}_{\infty , \infty}$ implies regularity

Pages: 1 – 4

DOI: https://dx.doi.org/10.4310/DPDE.2017.v14.n1.a1


Taoufik Hmidi (RMAR, Université de Rennes 1, Campus de Beaulieu, Rennes, France)

Dong Li (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)


We show that smallness of $\dot{B}^{-1}_{\infty , \infty}$ norm of solution to $d$-dimensional $(d \geq 3)$ incompressible Navier–Stokes prevents blowups.


critical Besov, blowup criteria, incompressible

2010 Mathematics Subject Classification

35B44, 35Q35

Published 31 January 2017