Angular Regularity and Strichartz Estimates for the Wave Equation

Jacob Sterbenz, Igor Rodnianski

Published 2004-02-12, updated 2005-03-04Version 2

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular momentum operators. In this setting, the range of (q,r) exponents vastly improves over what is available for the wave equations based on translation invariant derivatives of the initial data and the dispersive inequality. Two proofs of this result are given.