#### Vol. 6, No. 4, 2013

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Discrete Fourier restriction associated with KdV equations

### Yi Hu and Xiaochun Li

Vol. 6 (2013), No. 4, 859–892
##### Abstract

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg–de Vries equation with nonlinear term $F\left(u\right){\partial }_{x}u$ provided $F\in {C}^{5}$ and the initial data $\varphi \in {H}^{s}$ with $s>1∕2$.

##### Keywords
discrete Fourier restriction, KdV, local well-posedness
Primary: 35G25
Secondary: 42A16