A para-differential renormalization technique for nonlinear dispersive equations
Analysis of PDEs
2010-11-03 v1
Abstract
For \alpha \in (1,2) we prove that the initial-value problem \partial_t u+D^\alpha\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t; u(0)=\phi, is globally well-posed in the space of real-valued L^2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.
Keywords
Cite
@article{arxiv.0907.4649,
title = {A para-differential renormalization technique for nonlinear dispersive equations},
author = {Sebastian Herr and Alexandru D. Ionescu and Carlos E. Kenig and Herbert Koch},
journal= {arXiv preprint arXiv:0907.4649},
year = {2010}
}
Comments
42 pages, no figures