English

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 a(Dx)a(D_x) 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