Generalized and weighted Strichartz estimates

Jin-Cheng Jiang; Chengbo Wang; Xin Yu

doi:10.3934/cpaa.2012.11.1723

Article Contents

2012, Volume 11, Issue 5: 1723-1752. Doi: 10.3934/cpaa.2012.11.1723

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Generalized and weighted Strichartz estimates

1.
Institute of Mathematics, Academic Sinica, Taipei, Taiwan 10617
2.
Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218

Received: December 31, 2010

Revised: October 31, 2011

Published: August 2012

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Abstract

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 Schrödinger 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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Mathematics Subject Classification: 35L05, 35L70, 35J10.

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