Strichartz Estimates for the Schr\"odinger Equation

TL;DR

This paper reviews recent advances in Strichartz estimates for the Schrödinger equation across various function spaces, highlighting technical approaches and applications to well-posedness.

Contribution

It provides a comprehensive overview of the latest developments and techniques in establishing Strichartz estimates in diverse functional frameworks.

Findings

Establishment of Strichartz estimates in Lebesgue, Sobolev, Wiener amalgam, and modulation spaces.

Comparison of different technical methods used for deriving these estimates.

Application of estimates to prove well-posedness of the Schrödinger equation.

Abstract

The objective of this paper is to report on recent progress on Strichartz estimates for the Schr\"odinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in Wiener amalgam and modulation spaces. We present and compare the different technicalities. Then, we illustrate applications to well-posedness.