Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay

Nicolas Burq; Fabrice Planchon; John G. Stalker; A. Shadi Tahvildar-Zadeh

Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay

Analysis of PDEs 2010-09-13 v2

Authors: Nicolas Burq , Fabrice Planchon , John G. Stalker , A. Shadi Tahvildar-Zadeh

Abstract

We prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations.

Keywords

strichartz estimates schrodinger equation wave equation critical decay potentials weighted l^2 estimates morawetz estimates resolvent estimates

Cite

@article{arxiv.math/0401019,
  title  = {Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay},
  author = {Nicolas Burq and Fabrice Planchon and John G. Stalker and A. Shadi Tahvildar-Zadeh},
  journal= {arXiv preprint arXiv:math/0401019},
  year   = {2010}
}

Comments

18 pages, error corrected in the proof of Lemma 3.2

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