Persistence property in weighted Sobolev spaces for nonlinear dispersive equations

TL;DR

This paper extends a key interpolation lemma to demonstrate the persistence of solutions in weighted Sobolev spaces for nonlinear dispersive equations like the Korteweg-de Vries and nonlinear Schrödinger equations, even with low regularity.

Contribution

It generalizes the Abstract Interpolation Lemma and applies it to establish persistence properties for a broader class of nonlinear dispersive equations.

Findings

Persistence in weighted Sobolev spaces for KdV with low regularity

Extension of interpolation techniques to multidimensional models

Method applicable to various nonlinear dispersive equations

Abstract

We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted Sobolev space with low regularity in the weight. The method used can be applied for other nonlinear dispersive models, for instance the multidimensional nonlinear Schrodinger equation.