Local models and large scale statistics of the kuramoto-sivashinsky equation

Abstract We investigate the ability of local models of the one space dimensional Kuramoto-Sivashinsky (KS) equation, obtained either from ‘local’ wavelet projections or by projection on a small set of Fourier modes supported on a short subinterval, to reproduce coherent events typical of solutions of the same equation on a much longer interval. We also show that an effective equation preserving the statistics of the large scales of the KS equation can be obtained from a coarse-graining procedure based on the wavelet decomposition of the KS equation.

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