Analyticity for Kuramoto-Sivashinsky-type equations in two spatial dimensions
Date
2016Source
Mathematical Methods in the Applied SciencesVolume
39Issue
8Pages
2159-2178Google Scholar check
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I. Stratis In this work, we investigate the analyticity properties of solutions of Kuramoto-Sivashinsky-type equations in two spatial dimensions, with periodic initial data. In order to do this, we explore the applicability in three-dimensional models of a spectral method, which was developed by the authors for the one-dimensional Kuramoto-Sivashinsky equation. We introduce a criterion, which provides a sufficient condition for analyticity of a periodic function uâCâ, involving the rate of growth of â‡nu, in suitable norms, as n tends to infinity. This criterion allows us to establish spatial analyticity for the solutions of a variety of systems, including Topper-Kawahara, Frenkel-Indireshkumar, and Coward-Hall equations and their dispersively modified versions, once we assume that these systems possess global attractors. © 2015 John Wiley & Sons, Ltd.
DOI
10.1002/mma.3631Collections
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