A note on local well-posedness of generalized KdV type equations with dissipative perturbations

TL;DR

This paper establishes local well-posedness for generalized KdV equations with dissipative perturbations in low regularity Sobolev spaces using contraction mapping in time-weighted spaces.

Contribution

It provides new local well-posedness results for generalized KdV equations with dissipative terms in low regularity Sobolev spaces, employing a contraction mapping approach.

Findings

Well-posedness established in low regularity spaces

Use of contraction mapping in time-weighted spaces

Applicable to generalized KdV equations with dissipative perturbations

Abstract

In this note we report local well-posedness results for the Cauchy problems associated to generalized KdV type equations with dissipative perturbation for given data in the low regularity $L^2$-based Sobolev spaces. The method of proof is based on the {\em contraction mapping principle} employed in some appropriate time weighted spaces.