The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces

TL;DR

This paper investigates the well-posedness and decay properties of solutions to the dispersion generalized Benjamin-Ono equation within weighted Sobolev spaces, providing insights into solution uniqueness and decay rates.

Contribution

It establishes well-posedness results and sharp decay rates for solutions in weighted Sobolev spaces, advancing understanding of the equation's behavior.

Findings

Proved well-posedness in weighted Sobolev spaces.

Derived optimal decay rates for solutions.

Established unique continuation properties.

Abstract

We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well posedness results in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.