Generalized and weighted Strichartz estimates

TL;DR

This paper establishes new generalized and weighted Strichartz estimates for dispersive equations in Euclidean space, enabling progress on the Strauss conjecture at low regularity in low dimensions.

Contribution

It introduces a broad class of new Strichartz estimates, including weighted versions, applicable to various dispersive operators like Schrödinger and wave equations.

Findings

Proved generalized and weighted Strichartz estimates for multiple dispersive operators.

Applied these estimates to prove the Strauss conjecture with low regularity in dimensions 2 and 3.

Extended the understanding of dispersive PDEs through new analytical tools.

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 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.