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Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II
- DOI:
- 10.1080/03605300902793956
pages 203-232
Available online: 19 Mar 2009Abstract
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 0 ≤ ε ≤ 1, |v (x, t)| ≤ C 
r −1+ε |t|−ε/2 for − T 0 ≤ t < 0 and 0 < C < ∞ allowed to be large. We prove that v is regular at time zero.
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- Citation information:
- Available online: 19 Mar 2009
Author affiliations
- a Department of Mathematics and Taida Institute for Mathematical Sciences, National Taiwan University and National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan
- b Department of Mathematics, Harvard University, Cambridge, Massachusetts, USA
- c Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
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