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arXiv · 1302.6271

Smoothing properties of inhomogeneous equations via canonical transforms

Michael Ruzhansky·Mitsuru Sugimoto
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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 $a(D_x)$ with lower order terms are the benefit of our new method.

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Michael Ruzhansky, Mitsuru Sugimoto. 2013-02-25. Smoothing properties of inhomogeneous equations via canonical transforms. https://arxiv.org/abs/1302.6271

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