2010

The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes

Luk, Jonathan

Understand

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

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A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole
Jonathan Luk · 2010
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