Space-time estimates for the wave equations with singular potentials
type: Item
instance of: scholarly article
title: Space-time estimates for the wave equations with singular potentials
zbMATH Open document ID: 1152.35068
author: Jingyu Li
author: Kaijun Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-10-06T00:00:00Z
review text: The IVP for the wave equation with a time dependent potential \(V(x, t)\) is considered. The potential is allowed to have a singularity in the origin of the coordinates, is not necessarily differentiable but its supremum over all \(t\) has to be bounded by a special function depending on spatial dimension \(n\) and space variable \(x\). The dimension \(n\) is considered greater or equal to 3. In case the initial conditions belong to some Sobolev spaces, one proves the local regularity of solution and additional the Strichartz type estimate.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L10
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 5349084
zbMATH Keywords: wave equation
zbMATH Keywords: local regularity
zbMATH Keywords: Strichartz estimate
zbMATH Keywords: time dependent potential
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.03.078
OpenAlex ID: W2011588948
cites work: Asymptotic properties of solutions of differential equations with simple characteristics
cites work: Some dispersive estimates for Schrödinger equations with repulsive potentials
cites work: Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
cites work: Strichartz estimates for the wave and Schroedinger equations with potentials of critical decay
cites work: Q4434430
cites work: Maximal functions associated to filtrations
cites work: Local Smoothing Properties of Dispersive Equations
cites work: Decay Estimates for the Wave Equation with Potential
cites work: Q4745767
cites work: Endpoint Strichartz estimates
cites work: Small solutions to nonlinear Schrödinger equations
cites work: On the Zakharov and Zakharov-Schulman systems
cites work: Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
cites work: On some Schrödinger and wave equations with time dependent potentials
cites work: \(L^p\) estimates for the wave equation with the inverse-square potential
cites work: Q4185363
cites work: Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
cites work: Q4039228
cites work: Local regularity of solutions to wave equations with time-dependent potentials
cites work: Regularity of solutions to the Schrödinger equation
cites work: Q5475904
cites work: Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
cites work: Schrodinger Equations: Pointwise Convergence to the Initial Data
cites work: Existence of solutions for Schrödinger evolution equations
DOI: 10.1016/J.JMAA.2008.03.078
description: scientific article; zbMATH DE number 5349084