Analysis and Partial Differential Equations
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 $F(u)\p_x u$ provided F∈C5 and the initial data ϕ∈Hs with s>1/2.
Hu, Yi, Xiaochun Li.
"Discrete Fourier Restriction Associated with KdV Equations."
Analysis and Partial Differential Equations, 6 (4): 859-892.