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Time-global smoothing estimates for a class of dispersive equations with constant coefficients

Kei Morii Mathematical Institute, Tohoku University

TBD mathscidoc:1701.333132

Arkiv for Matematik, 46, (2), 363-375, 2006.12
We discuss smoothing effects of homogeneous dispersive equations with constant coefficients. In the case where the characteristic root is positively homogeneous, time-global smoothing estimates are known. It is also known that a dispersiveness condition is necessary for smoothing effects. We show time-global smoothing estimates where the characteristic root is not necessarily homogeneous. Our results give a sufficient condition so that lower order terms can be absorbed by the principal part, and also indicate that smoothing effects may be caused by lower order terms in the case where the dispersiveness condition fails to hold.
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@inproceedings{kei2006time-global,
  title={Time-global smoothing estimates for a class of dispersive equations with constant coefficients},
  author={Kei Morii},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203622902171941},
  booktitle={Arkiv for Matematik},
  volume={46},
  number={2},
  pages={363-375},
  year={2006},
}
Kei Morii. Time-global smoothing estimates for a class of dispersive equations with constant coefficients. 2006. Vol. 46. In Arkiv for Matematik. pp.363-375. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203622902171941.
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