Lower bound on the blow-up rate of the axisymmetric navier-stokes equations
Resource
International Mathematics Research Notices 2008 article ID rnn016
Journal
International Mathematics Research Notices
Journal Volume
2008
Journal Issue
1
Date Issued
2008
Author(s)
Abstract
Consider 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.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
02.pdf
Size
23.52 KB
Format
Adobe PDF
Checksum
(MD5):c3aaf5ba7bb22680fd8e234e47c22e73