Local well-posedness of periodic fifth order KdV type equations

TL;DR

This paper establishes local well-posedness for a class of periodic fifth order KdV-type equations with polynomial nonlinearities and introduces new Strichartz estimates to support the analysis.

Contribution

It proves local well-posedness for a broad class of fifth order dispersive equations with polynomial nonlinearities and derives new Strichartz estimates.

Findings

Proved local well-posedness for the equations.

Developed new Strichartz estimates.

Enhanced understanding of dispersive PDEs.

Abstract

In this paper, the local well-posedness of periodic fifth order dispersive equation with nonlinear term $P_1(u)\p_xu + P_2(u)\p_x u\p_xu $. Here $P_1(u)$ and $P_2(u)$ are polynomials of $u$. We also get some new Strichartz estimates.