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

This issue Previous Article Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal Next Article Instability of coupled systems with delay

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: January 2011

Revised: November 2011

Published: September 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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