Jim Colliander, Markus Keel, Gigliola Staffilani, Hideo Takaoka, Terence Tao
Published 2001-10-04, updated 2006-07-14Version 3
We prove an endpoint multilinear estimate for the $X^{s,b}$ 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. In particular we prove a multilinear estimate which completes the proof of global well-posedness for periodic KdV in a preceding paper (math.AP/0110045) down to the optimal regularity H^{-1/2}.
Comments: 39 pages. A correction to the Case 3 argument in Section 14
Journal: J. Funct. Anal. 211 (2004), 173-218
Vector analysis on fractals and applications
Analyzability in the context of PDEs and applications
Local well posedness for KdV with data in a subspace of $H^{-1}$ and applications to illposedness theory for KdV and mKdV
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