Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity
type: Item
instance of: scholarly article
title: Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity
zbMATH Open document ID: 1060.35121
author: Kenji Yajima
author: Guoping Zhang
published in: Journal of Differential Equations
publication date: 2004-08-19T00:00:00Z
review text: The smoothing properties of time-dependent linear Schrödinger operators with potentials growing super-quadratically are studied. Also, Strichartz type inequalities for these operators are proved which, as usual, can be applied to nonlinear Schrödinger equations. If the potential grows like a power of order \(m\) in the spatial variable the corresponding solution of the initial value problem (with initial data from state space) gains derivatives of order \(1/m\), and \(L(p,q)\)-norms of solutions can be estimated by derivatives of the initial data up to a specific order (Strichartz estimates). The proofs use a variety of methods, e.g. estimates of fundamental solutions of the corresponding equations, Calderon-Vaillancourt inequalities, scaled Hamiltonians, techniques of semi-classical analysis and pseudo-differential calculus, and results of Keel-Tao.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q20
zbMATH DE Number: 2092985
zbMATH Keywords: time-dependent linear Schrödinger operators
zbMATH Keywords: Strichartz type inequalities
zbMATH Keywords: Calderon-Vaillancourt inequalities
zbMATH Keywords: Hamiltonians
zbMATH Keywords: pseudo-differential calculus
reviewed by: Horst Lange
MaRDI profile type: Publication
full work available at URL: j.jde.2004.03.027
OpenAlex ID: W2022460729
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DOI: 10.1016/J.JDE.2004.03.027
description: scientific article; zbMATH DE number 2092985