Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations
Abstract
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random Gaussian initial data approximated by truncation of Fourier modes. These fine behaviors of nonlinear wave equations have not yet been observed numerically . In this article we perform numerical simulations of the one dimensional fractional cubic defocusing wave equation in a periodic setting. This allows us to explore energy subcritical and supercritial regimes. Our numerical results suggest that both norm inflation and probabilistic well-posedness can be observed numerically in energy sub-critical and super-critical regimes.
Keywords
Cite
@article{arxiv.2604.05938,
title = {Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations},
author = {Wandrille Ruffenach and Nikolay Tzvetkov},
journal= {arXiv preprint arXiv:2604.05938},
year = {2026}
}