Smoothing properties of inhomogeneous equations via canonical transforms
Analysis of PDEs
2015-10-16 v1 Functional Analysis
Abstract
The paper describes a new approach to global smoothing problems for inhomogeneous dispersive evolution equations based on an idea of canonical transformation. In our previous papers, we introduced such a method to show global smoothing estimates for homogeneous dispersive equations. It is remarkable that this method allows us to carry out a global microlocal reduction of equations to some low dimensional model cases. The purpose of this paper is to pursue the same treatment for inhomogeneous equations. Especially, time-global smoothing estimates for the operator with lower order terms are the benefit of our new method.
Keywords
Cite
@article{arxiv.1302.6271,
title = {Smoothing properties of inhomogeneous equations via canonical transforms},
author = {Michael Ruzhansky and Mitsuru Sugimoto},
journal= {arXiv preprint arXiv:1302.6271},
year = {2015}
}
Comments
16 pages. arXiv admin note: substantial text overlap with arXiv:math/0612274