Low-regularity invariant measure for the complex-valued mKdV
Analysis of PDEs
2026-03-20 v1
Abstract
In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an invariant measure supported at low-regularity. This work complements the work of Kenig et al., which constructed invariant measures supported in higher-regularity spaces for the non-renormalized mKdV. Due to the low-regularity of the support of the measure, we are forced to work in Fourier-Lebesgue spaces. The fact that we consider the complex-valued mKdV makes the problem more complicated than the real-valued case, which was previously considered.
Cite
@article{arxiv.2603.18310,
title = {Low-regularity invariant measure for the complex-valued mKdV},
author = {Zachary Lee and Nataša Pavlović and Gigliola Staffilani and Nicola Visciglia},
journal= {arXiv preprint arXiv:2603.18310},
year = {2026}
}