Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations. This estimate is optimal up to a logarithmic correction. The relevance of this estimate to turbulence and related results are also briefly discussed.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics