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Multilinear estimates for periodic KdV equations and applications

Jim Colliander·Markus Keel·Gigliola Staffilani·Hideo Takaoka·Terence Tao
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Abstract

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}.

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Jim Colliander, Markus Keel, Gigliola Staffilani, Hideo Takaoka, Terence Tao. 2006-07-14. Multilinear estimates for periodic KdV equations and applications. https://arxiv.org/abs/math/0110049

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