Generalized and weighted Strichartz estimates

Details Generalized and weighted Strichartz estimates Generalized and weighted Strichartz estimates

2010-08-31

arxiv.org/abs/1008.5397v2

Mathematics

Analysis of PDEs

Final version, to appear in the Communications on Pure and Applied Analysis. 33 pages. 2 more references added

Scientific paper

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schr\"odinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.

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