Multilinear estimates for periodic KdV equations, and applications

摘要

We prove an endpoint multilinear estimate for the X-s,X-b spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global well-posedness results below the energy norm. (C) 2003 Elsevier Inc. All rights reserved.