Stochastic estimates for the thin-film equation with thermal noise
Abstract
We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension and in the full subcritical regime of noise regularity. The prototype of the class of equations we study is the so-called thin-film equation with thermal noise, also commonly referred to in the literature as the stochastic thin-film equation. We derive an explicit expression for the form of the counterterm as a function of the film mobility which is in surprising agreement with the form conjectured in Remark 9.1 of Math. Comp. 92 (2023), 1931-976.
Keywords
Cite
@article{arxiv.2309.15829,
title = {Stochastic estimates for the thin-film equation with thermal noise},
author = {Rishabh S. Gvalani and Markus Tempelmayr},
journal= {arXiv preprint arXiv:2309.15829},
year = {2026}
}
Comments
New subsection comparing to previous literature, improved presentation of Theorem 2.16 and shortened proof, updated bibliography, 76 pages, 1 figure