A new mode reduction strategy for the generalized Kuramoto–Sivashinsky equation

Schmuck, M.; Pradas, M.; Pavliotis, G. A. and Kalliadasis, S. (2015). A new mode reduction strategy for the generalized Kuramoto–Sivashinsky equation. IMA Journal of Applied Mathematics, 80(2) pp. 273–301.

DOI: https://doi.org/10.1093/imamat/hxt041


Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented.

Viewing alternatives

Download history


Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions