Angular Regularity and Strichartz Estimates for the Wave Equation

Details Angular Regularity and Strichartz Estimates for the Wave Equation Angular Regularity and Strichartz Estimates for the Wave Equation

2004-02-12

arxiv.org/abs/math/0402192v2

Mathematics

Analysis of PDEs

34 pages. Updated with a simplified physical space proof by Igor Rodnianski

Scientific paper

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.

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