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arXiv · 1408.2020

On a nonlocal analog of the Kuramoto-Sivashinsky equation

Rafael Granero-Belinchón·John K. Hunter
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Abstract

We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order less than or equal to two, and long waves are destabilized by a backward fractional diffusion of lower order. We prove the global existence, uniqueness, and analyticity of solutions of the nonlocal equation and the existence of a compact attractor. Numerical results show that the equation has chaotic solutions whose spatial structure consists of interacting traveling waves resembling viscous shock profiles.

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Rafael Granero-Belinchón, John K. Hunter. 2015-01-06. On a nonlocal analog of the Kuramoto-Sivashinsky equation. https://doi.org/10.1088/0951-7715%2F28%2F4%2F1103

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