Analysis Seminar

The Strauss conjecture for the Minkowski spacetime in three dimensions states that the semilinear equation \[\Box u=|u|^p,\ u(0) =\epsilon f,\ \partial_t u(0) = \epsilon g\] has a global solution for all $f$ and$g$ smooth, compactly supported and $\epsilon$ small enough if $p > 1 + \sqrt{2}$. We prove a similar result in the context on Schwarzschild and Kerr with small angular momentum spacetimes.

This is joint work with H. Lindblad, J. Metcalfe, C. Sogge, and C. Wang.