On the regularity of solutions to a class of nonlinear dispersive equations

TL;DR

This paper investigates how the initial regularity of solutions to certain nonlinear dispersive equations influences their evolution, emphasizing the role of different function spaces in measuring this regularity.

Contribution

It provides new insights into the transfer of initial data regularity to solutions in nonlinear dispersive models, highlighting the importance of the choice of function spaces.

Findings

Regularity of initial data affects solution smoothness over time

Different function spaces influence regularity transfer

Results apply to specific classes of nonlinear dispersive equations

Abstract

We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is measured.