On local-in-time Strichartz estimates for the Schr\"odinger equation with singular potentials

Seongyeon Kim; Ihyeok Seo; Jihyeon Seok

On local-in-time Strichartz estimates for the Schr\"odinger equation with singular potentials

Analysis of PDEs 2021-02-24 v4

Authors: Seongyeon Kim , Ihyeok Seo , Jihyeon Seok

Abstract

There have been a lot of works concerning the Strichartz estimates for the perturbed Schr\"odinger equation by potential. These can be basically carried out adopting the well-known procedure for obtaining the Strichartz estimates from the weighted $L^2$ resolvent estimates for the Laplacian. In this paper we handle the Strichartz estimates without relying on the resolvent estimates. This enables us to consider various potential classes such as the Morrey-Campanato classes.

Keywords

strichartz estimates schrödinger equation singular potentials morrey-campanato classes local-in-time estimates

Cite

@article{arxiv.1910.14256,
  title  = {On local-in-time Strichartz estimates for the Schr\"odinger equation with singular potentials},
  author = {Seongyeon Kim and Ihyeok Seo and Jihyeon Seok},
  journal= {arXiv preprint arXiv:1910.14256},
  year   = {2021}
}

Comments

To appear in Math. Nachr., 9 pages

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