# Local well-posedness of nonlinear dispersive equations on modulation spaces

## TL;DR

This paper improves local well-posedness results for nonlinear dispersive equations like NLS, NLW, and NLKG using time-frequency analysis in modulation spaces, expanding understanding of solution behavior with specific initial data.

## Contribution

It introduces novel local well-posedness results for key dispersive equations in modulation spaces, leveraging advanced time-frequency analysis techniques.

## Key findings

- Enhanced well-posedness results for NLS, NLW, NLKG
- Application of modulation spaces in dispersive PDE analysis
- Use of time-frequency tools to improve solution existence

## Abstract

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces $M{p, 1}_{0,s}$.