2023/09/27 by Rishabh S. Gvalani, Gvalani, Rishabh S., Markus Tempelmayr +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H17 #60L30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2309.15829
openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension d≥ 1 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.