A sharp condition for the well-posedness of the linear KdV-type equation

TL;DR

This paper clarifies the well-posedness conditions for linear KdV-type equations by simplifying the ill-posedness argument to the constant dispersion case, correcting minor errors, and enhancing understanding.

Contribution

It provides a clearer, more transparent criterion for well-posedness of linear KdV-type equations, improving upon previous complex arguments.

Findings

Reduced the ill-posedness argument to the constant dispersion case

Corrected minor errors in the existing proofs

Enhanced clarity of the well-posedness conditions

Abstract

To make the illposedness argument more transparent the argument is rewritten to reduce the equation to the constant dispersion case. Minor errors are corrected. Accepted to the Proceedings of the AMS.