On large potential perturbations of the Schrödinger, wave and Klein-Gordon equations

DOI10.3934/CPAA.2020029zbMATH Open1428.35431arXiv1706.04840OpenAlexW2963862138MaRDI QIDQ2332321

Publication date: 4 November 2019

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Abstract: We prove a sharp resolvent estimate in scale invariant norms of Amgon--H"{o}rmander type for a magnetic Schr"{o}dinger operator on

m a t h b b R^{n}

,

n g e 3

�egin{equation*} L=-(partial+iA)^{2}+V end{equation*}with large potentials

A, V

of almost critical decay and regularity. The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schr"{o}dinger, wave and Klein--Gordon flows associated to

L

.

Full work available at URL: https://arxiv.org/abs/1706.04840

zbMATH Keywords

Schrödinger equation resolvent estimates Strichartz estimates local energy decay dispersive equations

Mathematics Subject Classification ID

Wave equation (35L05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (9)

Global Strichartz estimates for an inhomogeneous Maxwell system ⋮ Semilinear Schrödinger equations with a critical scale of the singular electromagnetic field ⋮ On Morawetz estimates with time-dependent weights for the Klein-Gordon equation ⋮ 3D quadratic NLS equation with electromagnetic perturbations ⋮ Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators ⋮ Strichartz estimates and local regularity for the elastic wave equation with singular potentials ⋮ Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential ⋮ Spectral multipliers for magnetic Schrödinger operators ⋮ On pointwise decay of waves

This page was built for publication: On large potential perturbations of the Schrödinger, wave and Klein-Gordon equations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2332321)