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

### Jonathan Luk

Princeton University, USA

## 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 $\{r\leq \frac{t}{4}\}$.

## Cite this article

Jonathan Luk, The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1629–1700

DOI 10.4171/JEMS/400