Global existence of null-form wave equations in exterior domains
type: Item
instance of: scholarly article
title: Global existence of null-form wave equations in exterior domains
zbMATH Open document ID: 1138.35065
author: Jason Metcalfe
author: Christopher D. Sogge
published in: Mathematische Zeitschrift
publication date: 2008-01-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0611489
review text: The major innovations of this paper regard the variable-coefficient Keel-Smith-Sogge (KSS) estimate. Firstly, the authors prove the KSS estimate for the perturbed wave equaton in the multiple speed setting. Having such estimates for the perturbed equation allows the authors to apply the KSS estimates even for terms of the highest order. This was not previously possible for quasilinear equations as there was a loss of regularity resulting from the occurrence of second derivatives. As such, the authors may prove global existence using only energy methods. In particular, the decay estimates that the authors shall employ do not require direct estimation of the fundamental solution of the linear wave equation. Thus the authors provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5227340
zbMATH Keywords: quasilinear wave equations
zbMATH Keywords: Keel-Smith-Sogge estimate
zbMATH Keywords: null condition
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2594866359
arXiv ID: math/0611489
cites work: Q4224971
cites work: Global solutions of nonlinear hyperbolic equations for small initial data
cites work: An elementary proof of global or almost global existence for quasi-linear wave equations
cites work: A Remark on the Almost Global Existence Theorems of Keel, Smith and Sogge
cites work: Lectures on nonlinear hyperbolic differential equations
cites work: Global existence for a class of systems of nonlinear wave equations in three space dimensions
cites work: Global existence for systems of wave equations with nonresonant nonlinearities and null forms
cites work: Global existence for a quasilinear wave equation outside of star-shaped domains
cites work: Almost global existence for some semilinear wave equations
cites work: Almost global existence for quasilinear wave equations in three space dimensions
cites work: Uniform decay estimates and the lorentz invariance of the classical wave equation
cites work: Q3733338
cites work: Q4884687
cites work: Global existence of classical solutions to systems of nonlinear wave equations with different speeds of propagation
cites work: Exponential decay of solutions of the wave equation in the exterior of a star‐shaped obstacle
cites work: Q4827074
cites work: Global Existence of Solutions to Multiple Speed Systems of Quasilinear Wave Equations in Exterior Domains
cites work: Q3379023
cites work: Hyperbolic trapped rays and global existence of quasilinear wave equations
cites work: Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions
cites work: Long-Time Existence of Quasilinear Wave Equations Exterior to Star-Shaped Obstacles via Energy Methods
cites work: The decay of solutions of the exterior initial-boundary value problem for the wave equation
cites work: Nonresonance and global existence of prestressed nonlinear elastic waves
cites work: Global existence for systems of nonlinear wave equations in 3D with multiple speeds
cites work: Q5475904
cites work: Q4462264
cites work: Q4673258
cites work: Dispersal of waves vanishing on the boundary of an exterior domain
cites work: Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions
DOI: 10.1007/S00209-006-0083-2
description: scientific article