Remark on the semilinear ill-posedness for a periodic higher order KP-I equation

TL;DR

This paper demonstrates that the periodic fifth-order KP-I equation exhibits semilinear ill-posedness on certain irrational tori, with the flow map lacking local uniform continuity in the energy space.

Contribution

It provides new insights into the ill-posedness of higher-order KP-I equations on irrational tori, highlighting limitations of well-posedness in the energy space.

Findings

Flow map is not locally uniformly continuous on irrational tori.

Ill-posedness persists even on hyperplanes of fixed x-mean value.

Results extend understanding of KP-I equation behavior in periodic settings.

Abstract

We prove that, for some irrational torus, the flow map of the periodic fifth-order KP-I equation is not locally uniformly continuous on the energy space, even on the hyperplanes of fixed x-mean value.