Archive for November, 2018

Dafermos and Rodnianski introduced an {r^p}-weighted vector field method to obtain boundedness and decay of solutions to wave equations on a Lorentzian background, avoiding to use global vector field multipliers and commutators with weights in {t} and thus proving to be more robust in dealing with black holes such as in Schwarzschild and Kerr background metrics. The approach has found numerous applications; see, for instance, Dafermos-Rodnianski, Moschidis, or Keir for many insightful discussions. In this blog post, I will give some basic details of this approach, based on lecture notes of S. Klainerman, focusing mostly on the flat Minkowski spacetime.



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