Discrete Fourier restriction associated with KdV equations

TL;DR

This paper investigates discrete Fourier restriction related to KdV equations, deriving new Strichartz estimates and proving local well-posedness for a class of periodic generalized KdV equations with specific nonlinearities.

Contribution

It introduces new Strichartz estimates and establishes local well-posedness for generalized KdV equations with nonlinear terms in a certain regularity class.

Findings

New Strichartz estimates for KdV-related discrete Fourier restriction

Local well-posedness for periodic generalized KdV with nonlinear term F(u)∂_x u

Well-posedness holds for initial data in H^s with s>1/2

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(u)\p_x u$ provided $F\in C^5$ and the initial data $\phi\in H^s$ with $s>1/2$.