On a non-linear 2D fractional wave equation

TL;DR

This paper extends the analysis of a 2D non-linear fractional wave equation with stochastic forcing to rougher noise, highlighting the limitations of Wick-renormalisation and employing a third-order expansion for better understanding.

Contribution

It introduces a third-order expansion to handle rougher fractional noise in a 2D non-linear wave equation, extending prior results and analyzing renormalisation limits.

Findings

Extended the model to rougher noise scenarios.

Identified the limits of Wick-renormalisation in this context.

Demonstrated the effectiveness of third-order expansion techniques.

Abstract

We pursue the investigations initiated in [Aur{\'e}lien Deya: A non-linear wave equation with fractional perturbation (2017)] about a wave-equation model with quadratic perturbation and stochastic forcing given by a space-time fractional noise. We focus here on the two-dimensional situation and therein extend the results of the previous reference to a rougher noise, through the use of a third-order expansion. We also point out the limits of the Wick-renormalisation procedure in this case.