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

Jonathan Luk

Journal of the European Mathematical Society (2013)

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

Abstract

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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 { r ≤ t 4 } .

How to cite

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Luk, 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 -

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