# Time-decay and Strichartz estimates for the Benjamin-Bona-Mahony equation and existence of solutions on modulation spaces

## TL;DR

This paper establishes time-decay and Strichartz estimates for the Benjamin-Bona-Mahony equation within modulation spaces, leading to new results on the existence of solutions with rough data, surpassing previous Sobolev space findings.

## Contribution

It introduces novel estimates in modulation spaces for the Benjamin-Bona-Mahony equation, enhancing understanding of solution existence with less regular initial data.

## Key findings

- Derived time-decay estimates in modulation spaces
- Established Strichartz estimates for the equation
- Proved existence of solutions with rough initial data

## Abstract

In this paper we derive time-decay and Strichartz estimates for the generalized Benjamin-Bona-Mahony equation on the framework of modulation spaces $M^s_{p,q}.$ We use this results to analyze the existence of local and global solutions of the corresponding Cauchy problem with rough data in modulation spaces. The results improve known results in Sobolev spaces in some sense.