Angular regularity and Strichartz estimates for the wave equation. (English) Zbl 1072.35048

Sterbenz, Jacob

Int. Math. Res. Not. 2005, No. 4, 187-231 (2005).

Different Strichartz type estimates, i.e. space-time estimates for solutions of the wave equation, that improve classical Strichartz estimates, are proved. Also improvements, over the usual multilinear estimates for the wave equation, are done for multilinear type estimates involving weighted angular regularity on one or any number of factors. These estimates are obtained by using Tao’s dual scale machine for generating multilinear estimates. Up to a small loss of angular regularity the estimates are sharp. As standard reference for the content of this work is given the paper of M. Keel and T. Tao [Am. J. Math. 120, No. 5, 955–980 (1998; Zbl 0922.35028)].

Reviewer: Claudia Simionescu-Badea (Wien)

MSC:

35B45	A priori estimates in context of PDEs
35L05	Wave equation

Keywords:

multilinear estimates; Tao’s dual scale machine

Citations:

Zbl 0922.35028