Global Well-Posedness for the Fifth-Order KdV Equation in H-1 (R)

摘要

We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in H-1 (R). Global well-posedness in L-2 (R) was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp L-2 threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.