\(L^p\) estimates for the wave equation with the inverse-square potential
type: Item
instance of: scholarly article
title: \(L^p\) estimates for the wave equation with the inverse-square potential
zbMATH Open document ID: 1031.35092
author: John Stalker
author: A. Shadi Tahvildar-Zadeh
author: Fabrice Planchon
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-03-07T00:00:00Z
review text: The authors study the following linear wave equation \[ \begin{gathered} \square_n u+{a\over|x|^2} u= h(x,t),\\ u(x,0)= f(x),\\ \partial_t u(x,0)= g(x),\end{gathered}\tag{1} \] where \(\square_n= \partial^2_t- \Delta_n\) is the D'Alembertian in \(\mathbb{R}^{n+1}\) and \(a\) is a real number. They prove that Strichartz-type \(L^p\) estimates hold for solutions of the (1), under the additional assumption that the Cauchy data are spherically symmetric. Based on this estimate the authors prove global well-posedness in the critical norm for a nonlinear wave equation.
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1890746
zbMATH Keywords: spherically symmetric Cauchy data
zbMATH Keywords: Strichartz-type estimates
zbMATH Keywords: global well-posedness
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.427
OpenAlex ID: W2017513808
DOI: 10.3934/DCDS.2003.9.427
description: scientific article; zbMATH DE number 1890746