The Hyperboloidal Foliation Method

By: Philippe G Lefloch, Yue Ma

Write A Review

eText | 27 November 2014

At a Glance

ePUB
160 Pages

eText

$45.10

or 4 interest-free payments of $11.28 with

or

Instant online reading in your Booktopia eTextbook Library *

The “Hyperboloidal Foliation Method” introduced in this monograph is based on a (3 + 1) foliation of Minkowski spacetime by hyperboloidal hypersurfaces. This method allows the authors to establish global-in-time existence results for systems of nonlinear wave equations posed on a curved spacetime. It also allows to encompass the wave equation and the Klein-Gordon equation in a unified framework and, consequently, to establish a well-posedness theory for a broad class of systems of nonlinear wave-Klein-Gordon equations. This book requires certain natural (null) conditions on nonlinear interactions, which are much less restrictive that the ones assumed in the existing literature. This theory applies to systems arising in mathematical physics involving a massive scalar field, such as the Dirac-Klein-Gordon systems.

Contents:

Introduction
The Hyperboloidal Foliation and the Bootstrap Strategy
Decompositions and Estimates for the Commutators
The Null Structure in the Semi-Hyperboloidal Frame
Sobolev and Hardy Inequalities on Hyperboloids
Revisiting Scalar Wave Equations
Fundamental L^∞ and L² Estimates
Second-Order Dervatives of the Wave Components
Null Forms and Decay in Time
L² Estimate on the Interaction Terms
The Local Well-Posedness Theory
Bibliography

Readership: Graduate students and researchers in analysis and differential equations. This book could serve as part of graduate course on nonlinear wave equations.