Mixed norm estimates of Schr\"{o}dinger waves and their applications

TL;DR

This paper establishes mixed norm estimates for Schrödinger waves and applies these results to analyze smoothing effects and global well-posedness in mass-critical nonlinear Schrödinger equations.

Contribution

It introduces new mixed norm estimates for Schrödinger waves and demonstrates their application to nonlinear Schrödinger equations with critical mass nonlinearities.

Findings

Proved mixed norm estimates for Schrödinger waves.

Applied estimates to smoothing properties of solutions.

Established global well-posedness results for critical nonlinear Schrödinger equations.

Abstract

In this paper we establish mixed norm estimates of interactive Schr\"{o}dinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schr\"{o}dinger equations with mass critical nonlinearity.