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- W2949304651 abstract "We prove two new mixed sharp bilinear estimates of Schrodinger-Airy type. In particular, we obtain the local well-posedness of the Cauchy problem of the Schrodinger - Kortweg-deVries (NLS-KdV) system in the emph{periodic setting}. Our lowest regularity is $H^{1/4}times L^2$, which is somewhat far from the naturally expected endpoint $L^2times H^{-1/2}$. This is a novel phenomena related to the periodicity condition. Indeed, in the continuous case, Corcho and Linares proved local well-posedness for the natural endpoint $L^2times H^{-{3/4}+}$. Nevertheless, we conclude the global well-posedness of the NLS-KdV system in the energy space $H^1times H^1$ using our local well-posedness result and three conservation laws discovered by M. Tsutsumi." @default.
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- W2949304651 date "2005-11-19" @default.
- W2949304651 modified "2023-09-27" @default.
- W2949304651 title "Rough solutions for the periodic Schrodinger - Kortweg-deVries system" @default.
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