# The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 5, page 1629-1700
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topLuk, Jonathan. "The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes." Journal of the European Mathematical Society 015.5 (2013): 1629-1700. <http://eudml.org/doc/277494>.

@article{Luk2013,

abstract = {We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region $\lbrace r\le \frac\{t\}\{4\}\rbrace $.},

author = {Luk, Jonathan},

journal = {Journal of the European Mathematical Society},

keywords = {Kerr spacetime; wave equation; null condition; global existence; semilinear equation; Kerr spacetime; wave equation; null condition; global existence; semilinear equation},

language = {eng},

number = {5},

pages = {1629-1700},

publisher = {European Mathematical Society Publishing House},

title = {The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes},

url = {http://eudml.org/doc/277494},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Luk, Jonathan

TI - The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 5

SP - 1629

EP - 1700

AB - We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region $\lbrace r\le \frac{t}{4}\rbrace $.

LA - eng

KW - Kerr spacetime; wave equation; null condition; global existence; semilinear equation; Kerr spacetime; wave equation; null condition; global existence; semilinear equation

UR - http://eudml.org/doc/277494

ER -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.