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Structure of Singularities of 3D Axi-symmetric Navier-Stokes Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lei, Zhen Zhang, Qi S. |
| Copyright Year | 2010 |
| Abstract | Let $v$ be a solution of the axially symmetric Navier-Stokes equation. We determine the structure of certain (possible) maximal singularity of $v$ in the following sense. Let $(x_0, t_0)$ be a point where the flow speed $Q_0 = |v(x_0, t_0)|$ is comparable with the maximum flow speed at and before time $t_0$. We show after a space-time scaling with the factor $Q_0$ and the center $(x_0, t_0)$, the solution is arbitrarily close in $C^{2, 1, \alpha}_{{\rm local}}$ norm to a nonzero constant vector in a fixed parabolic cube, provided that $r_0 Q_0$ is sufficiently large. Here $r_0$ is the distance from $x_0$ to the $z$ axis. Similar results are also shown to be valid if $|r_0v(x_0, t_0)|$ is comparable with the maximum of $|rv(x, t)|$ at and before time $t_0$. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1008.4172v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
