Anisotropic Estimates for the Two-Dimensional Kuramoto–Sivashinsky Equation

We address the global solvability of the Kuramoto–Sivashinsky equation in a rectangular domain [ 0 , L 1 ] × [ 0 , L 2 ] . We give sufficient conditions on the width L 2 of the domain, depending on the length L 1 , so that the obtained solutions are global. Our proofs are based on anisotropic estima...

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Veröffentlicht in:	Journal of dynamics and differential equations 2014-09, Vol.26 (3), p.461-476
Hauptverfasser:	Benachour, Said, Kukavica, Igor, Rusin, Walter, Ziane, Mohammed
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis of PDEs Applications of Mathematics Mathematical Physics Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations
Online-Zugang:	Volltext
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Zusammenfassung:	We address the global solvability of the Kuramoto–Sivashinsky equation in a rectangular domain [ 0 , L 1 ] × [ 0 , L 2 ] . We give sufficient conditions on the width L 2 of the domain, depending on the length L 1 , so that the obtained solutions are global. Our proofs are based on anisotropic estimates.
ISSN:	1040-7294 1572-9222
DOI:	10.1007/s10884-014-9372-3