Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier-Stokes Equations II

摘要

Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in 3 with non-trivial swirl. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies, for some 01, |v (x, t)|C* r-1+ |t|-/2 for-T0t0 and 0C* allowed to be large. We prove that v is regular at time zero.