Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a...Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a general theorem in Banach spaces asserting that linear instability implies nonlinear instability.展开更多
基金Project Supported in part by NSFGrant DMS-0071838.
文摘Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a general theorem in Banach spaces asserting that linear instability implies nonlinear instability.