Global well-posedness for periodic generalized KdV equation

Abstract

In this paper, we show the global well-posedness for periodic gKdV equations in the space $H^s(\mathbb{T})$, $s\ge \frac{1}{2}$ for quartic case, and $s>\frac{5}{9}$ for quintic case. These improve the previous results of I-team in 2004. In particular, the result is sharp for quintic case. The main approaches are the I-method combining with the resonance decomposition developed by Miao et al in 2010, and a bilinear Strichartz estimate in periodic setting.

Some changes on expression in English

References in corpus (3)

• Global well-posedness for Schrödinger equation with derivative in $H^{1/2}(\mathbb{R})$
• Global rough solutions to the critical generalized KdV equation
• The low regularity global solutions for the critical generalized KdV equation