Speaker: Mihalis Dafermos (Princeton University)

Title: Quasilinear wave equations on asymptotically flat spacetimes with applications to general subextremal Kerr black holes

Abstract: I will describe a general method to treat non-linear stability problems for quasilinear wave equations on asymptotically flat background spacetimes, provided the nonlinearities have good structure at infinity of the type present in many physically important examples. The method requires two elements as input, both of which refer only to the linearisation of the equation around the trivial solution: (i) an appropriate integrated local energy decay estimate and (ii) the existence of an energy current possessing certain weak coercivity properties. In addition to unifying many previous results, the method yields the first non-linear stability statement for quasilinear equations on Kerr black holes in the full subextremal range |a| < M.  This is joint work with Gustav Holzegel, Igor Rodnianski and Martin Taylor.