Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II

Details Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II

2007-09-26

arxiv.org/abs/0709.4230v2

Communications in Partial Differential Equations, 34:3, 203 - 232 (2009)

Mathematics

Analysis of PDEs

More explanations and a new appendix

Scientific paper

10.1080/03605300902793956

Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in $\R^3$ with non-trivial swirl. Let $z$ denote the axis of symmetry and $r$ measure the distance to the z-axis. Suppose the solution satisfies either $|v (x,t)| \le C_*{|t|^{-1/2}} $ or, for some $\e > 0$, $|v (x,t)| \le C_* r^{-1+\epsilon} |t|^{-\epsilon /2}$ for $-T_0\le t < 0$ and $0

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