Chen, C.-C.Strain, R. M.Yau, Horng-TzerTsai, T.-P.2017-05-182010Chen, C.-C., R. M. Strain, H.-T. Yau, and T.-P. Tsai. 2010. “Lower Bound on the Blow-up Rate of the Axisymmetric Navier-Stokes Equations.” International Mathematics Research Notices (July 8). doi:10.1093/imrn/rnn016.1073-7928http://nrs.harvard.edu/urn-3:HUL.InstRepos:32706740Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in R 3 with non-trivial swirl. Such solutions are not known to be globally defined, but it is shown in [11, 1] that they could only blow up on the axis of symmetry. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies the pointwise scale invariant bound |v(x, t)| ≤ C∗(r 2 − t) −1/2 for −T0 ≤ t < 0 and 0 < C∗ < ∞ allowed to be large, we then prove that v is regular at time zero.en-USJournal Article2017-05-1810.1093/imrn/rnn016