Abstract
Time-averages are common observables in analysis of experimental data and numerical simulations of physical systems. We describe a straightforward framework for studying time-averages of dynamical systems whose solutions exhibit fast oscillatory behaviors. Time integration averages out the oscillatory part of the solution that is caused by the large skew-symmetric operator. Then, the time-average of the solution stays close to the kernel of this operator. The key assumption in this framework is that the inverse of the large operator is a bounded mapping between certain Hilbert spaces modular the kernel of the operator itself. This assumption is verified for several examples of time-dependent PDEs.
Original language | English (US) |
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Pages (from-to) | 1151-1162 |
Number of pages | 12 |
Journal | Discrete and Continuous Dynamical Systems - Series S |
Volume | 6 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2013 |
Keywords
- Coherent structures
- Mathematical geosciences
- Time-averages
- Waves
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics