We prove an endpoint multilinear estimate for the Xs,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.
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Keywords: Korteweg–de Vries equation; Nonlinear dispersive equations; Bilinear estimates; Multilinear harmonic analysis *Corresponding author. E-mail address: email@example.com (J. Colliander). 1Supported in part by N.S.F. Grant DMS 0100595 and N.S.E.R.C Grant RGPIN 250233-03. 2Supported in part by N.S.F. Grant DMS 9801558. 3Supported in part by N.S.F. Grant 0100375 and by grants from Hewlett and Packard and the Sloan Foundation. 4Supported in part by J.S.P.S. Grant No. 13740087. 5Clay Prize Fellow and is supported in part by grants from the Packard Foundation.
- Bilinear estimates
- Korteweg-de Vries equation
- Multilinear harmonic analysis
- Nonlinear dispersive equations