Global well-posedness for higher-order Schr\"odinger equations in weighted $L^2$ spaces

Youngwoo Koh; Ihyeok Seo

Global well-posedness for higher-order Schr\"odinger equations in weighted $L^2$ spaces

Analysis of PDEs 2015-03-26 v2

Authors: Youngwoo Koh , Ihyeok Seo

Abstract

We obtain the global well-posedness for Schr\"odinger equations of higher orders in weighted $L^2$ spaces. This is based on weighted $L^2$ Strichartz estimates for the corresponding propagator with higher-order dispersion. Our method is also applied to the Airy equation which is the linear component of Korteweg-de Vries type equations.

Keywords

Schr\"odinger equations higher-order global well-posedness weighted L^2 spaces Strichartz estimates Airy equation Korteweg-de Vries equations

Cite

@article{arxiv.1403.2915,
  title  = {Global well-posedness for higher-order Schr\"odinger equations in weighted $L^2$ spaces},
  author = {Youngwoo Koh and Ihyeok Seo},
  journal= {arXiv preprint arXiv:1403.2915},
  year   = {2015}
}

Comments

To appear in Comm. Partial Differential Equations, 15 pages

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