On Stability of Blow-Up Solutions of the Burgers Vortex Type for the Navier-Stokes Equations with a Linear Strain
Abstract
We study the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known that the system admits solutions which blow up in finite time and whose profiles are in a backward self-similar form of the familiar Burgers vortices. In this paper it is shown that the existing stability theory of the Burgers vortex leads to the stability of these blow-up solutions as well. The secondary blow-up is also observed when the strain rate is relatively weak.
- Publication:
-
Journal of Mathematical Fluid Mechanics
- Pub Date:
- December 2019
- DOI:
- 10.1007/s00021-019-0450-5
- arXiv:
- arXiv:1807.10341
- Bibcode:
- 2019JMFM...21...46M
- Keywords:
-
- Navier–Stokes equations;
- Blow-up solutions;
- Burgers vortex;
- Stability;
- Backward self-similarity;
- 35A01;
- 35B35;
- 35B40;
- 35B44;
- 35Q30;
- 35Q35;
- 76D05;
- 76E30;
- Mathematics - Analysis of PDEs;
- 35A01;
- 35B35;
- 35B40;
- 35B44;
- 35Q30;
- 35Q35;
- 76D05;
- 76E30
- E-Print:
- 25 pages