Dissipation enhancement by transport noise for stochastic $p$-Laplace equations

TL;DR

This paper demonstrates that transport noise increases dissipation in stochastic p-Laplace equations on the torus, with effects observed both on average and along individual paths.

Contribution

It introduces the effect of transport noise on dissipation enhancement in stochastic p-Laplace equations, a novel insight in this context.

Findings

Transport noise enhances dissipation in the stochastic p-Laplace equation.

Dissipation enhancement is observed in both averaged and pathwise senses.

The results are established on the torus or dimensions d 2.

Abstract

The stochastic $p$-Laplace equation with multiplicative transport noise is studied on the torus $\mathbb T^d\, (d\geq 2)$. It is shown that the dissipation is enhanced by transport noise in both the averaged sense and the pathwise sense.