On the Cauchy problem for quasi-linear Hamiltonian KdV-type equations

TL;DR

This paper establishes local well-posedness for a broad class of quasilinear Hamiltonian KdV-type equations with periodic boundary conditions, enhancing previous results by generalizing the equations and relaxing initial data regularity.

Contribution

It extends prior work by considering a larger class of equations and requiring less regularity on initial data for well-posedness.

Findings

Proves local existence and uniqueness of solutions.

Shows continuous dependence on initial data.

Generalizes previous well-posedness results.

Abstract

We prove local in time well-posedness for a class of quasilinear Hamiltonian KdV-type equations with periodic boundary conditions, more precisely we show existence, uniqueness and continuity of the solution map. We improve the previous result in \cite{Mietka}, generalising the considered class of equations and improving the regularity assumption on the initial data.