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
The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the line...The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.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.
文摘The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.
