Unconditional Well-posedness for the MMT Equation on the Torus

Mahendra Panthee; James Patterson; Yuzhao Wang

Unconditional Well-posedness for the MMT Equation on the Torus

Analysis of PDEs 2026-06-26 v1

Authors: Mahendra Panthee , James Patterson , Yuzhao Wang

Abstract

We consider the initial value problem (IVP) for a two-parameter family of derivative nonlinear Schr\"odinger equations on the torus, known as the Majda-McLaughlin-Tabak (MMT) model arising in weak wave turbulence theory. For positive derivative order, we show that the flow map is not $C^3$ at the origin. Using an enhanced energy method, we prove unconditional local well-posedness in Sobolev spaces. At the energy regularity, conservation of the Hamiltonian and a mass-type quantity yields unconditional global well-posedness.

Keywords

majda-mclaughlin-tabak equation derivative nonlinear schrödinger well-posedness torus energy method weak wave turbulence

Cite

@article{arxiv.2606.28290,
  title  = {Unconditional Well-posedness for the MMT Equation on the Torus},
  author = {Mahendra Panthee and James Patterson and Yuzhao Wang},
  journal= {arXiv preprint arXiv:2606.28290},
  year   = {2026}
}