Tianyuan Mathematical Center
in Southwest China

2018 Thematic Program (II)

Local dynamics near the solitary waves of the supercritical gKDV equations

[TMCSC]

June 21, 2018  16:00-17:00

W303  School of Mathematics, Sichuan University

SPEAKER

Jiayin Jin (Georgia Institute of Technology)

ABSTRCT

We study the dynamics of the supercritical gKDV equations near solitary waves in the energy space H1. We construct smooth local center-stable, center-unstable and center manifolds near the manifold of solitary waves and give a detailed description of the local dynamics near solitary waves. In particular, the instability is characterized as following: any forward flow not starting from the center-stable manifold will leave a neighborhood of the manifold of solitary waves exponentially fast. Moreover, orbital stability is proved on the center manifold, which implies the uniqueness of the center manifold and the global existence of solutions on it. This is a joint work with Zhiwu Lin and Chongchun Zeng.

ORGANIZERS

Kening Lu (Sichuan University)

Weinian Zhang (Sichuan University)

Wen Huang (Sichuan University)

Zeng Lian (Sichuan University)

Xiaohu Wang (Sichuan University)

Linfeng Zhou (Sichuan University)

Jun Shen (Sichuan University)

SUPPORTED BY

Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University