On the vanishing viscosity limit in a disk
Abstract
We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically in the unit disk, we show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the viscosity of the time-space average of the energy of u in a boundary layer of width proportional to the viscosity due to modes (eigenfunctions of the Stokes operator) whose frequencies in the radial or the tangential direction lie between L and M. Here, L must be of order less than 1/(viscosity) and M must be of order greater than 1/(viscosity).
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2006
- DOI:
- 10.48550/arXiv.math-ph/0612027
- arXiv:
- arXiv:math-ph/0612027
- Bibcode:
- 2006math.ph..12027K
- Keywords:
-
- Mathematical Physics;
- 76D05;
- 76B99;
- 76D99
- E-Print:
- Mathematische Annalen, 343:701-726, 2009