Smoothing and Strichartz estimates for degenerate Schrödinger-type equations

Fuente: arXiv
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Main Authors: Federico, Serena, Ruzhansky, Michael
Format: Preprint
Published: 2020
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author Federico, Serena
Ruzhansky, Michael
author_facet Federico, Serena
Ruzhansky, Michael
contents In this paper we focus on the validity of some fundamental estimates for time-degenerate Schrödinger-type operators. On one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison principles (that we shall obtain here). On the other hand, we prove weighted Strichartz-type estimates for time-degenerate Scrhödinger operators and apply them to the local well-posedness of the semilinear Cauchy problem. Most of our results apply to nondegenerate operators as well, recovering, in these cases, the well-known standard results.
format Preprint
id arxiv_https___arxiv_org_abs_2005_01622
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Smoothing and Strichartz estimates for degenerate Schrödinger-type equations
Federico, Serena
Ruzhansky, Michael
Analysis of PDEs
In this paper we focus on the validity of some fundamental estimates for time-degenerate Schrödinger-type operators. On one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison principles (that we shall obtain here). On the other hand, we prove weighted Strichartz-type estimates for time-degenerate Scrhödinger operators and apply them to the local well-posedness of the semilinear Cauchy problem. Most of our results apply to nondegenerate operators as well, recovering, in these cases, the well-known standard results.
title Smoothing and Strichartz estimates for degenerate Schrödinger-type equations
topic Analysis of PDEs
url https://arxiv.org/abs/2005.01622