Anisotropic estimates for the two dimensional Kuramoto-Sivashinsky equation

Saïd Benachour (1) , Igor Kukavica (2) , Walter Rusin (3) , Mohammed Ziane (3)

1 IECL - Institut Élie Cartan de Lorraine
2 Partial Differential Equations
3 USC - University of Southern California

We address the global solvability of the Kuramoto-Sivashinsky equation in a rectangular domain. We give sufficient conditions on the width L2 of the domain,depending on the length L1, so that the obtained solutions are global. Our proofs are based on anisotropic estimates.

Mots clés: Global existence.; anisotropic estimates; Kuramoto-Sivashinsky equation; Global existence

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Saïd Benachour, Igor Kukavica, Walter Rusin, Mohammed Ziane. Anisotropic estimates for the two dimensional Kuramoto-Sivashinsky equation. Journal of Dynamics and Differential Equations, 2014, 26, pp.461-476. ⟨10.1007/s10884-014-9372-3⟩. ⟨hal-00790207⟩