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2014 Large-time blowup for a perturbation of the cubic Szegő equation
Haiyan Xu
Anal. PDE 7(3): 717-731 (2014). DOI: 10.2140/apde.2014.7.717

Abstract

We consider the following Hamiltonian equation on a special manifold of rational functions:

i t u = Π ( | u | 2 u ) + α ( u | 1 ) , α ,

where Π denotes the Szegő projector on the Hardy space of the circle S1. The equation with α=0 was first introduced by Gérard and Grellier as a toy model for totally nondispersive evolution equations. We establish the following properties for this equation. For α<0, any compact subset of initial data leads to a relatively compact subset of trajectories. For α>0, there exist trajectories on which high Sobolev norms exponentially grow in time.

Citation

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Haiyan Xu. "Large-time blowup for a perturbation of the cubic Szegő equation." Anal. PDE 7 (3) 717 - 731, 2014. https://doi.org/10.2140/apde.2014.7.717

Information

Received: 19 July 2013; Accepted: 28 April 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1302.37042
MathSciNet: MR3227431
Digital Object Identifier: 10.2140/apde.2014.7.717

Subjects:
Primary: 35B44, 37J35, 47B35

Rights: Copyright © 2014 Mathematical Sciences Publishers

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