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Peer-reviewedCC BYCommunications in Mathematical Physics

Stochastic Estimates for the Thin-Film Equation with Thermal Noise

  • Rishabh S. Gvalani1
  • Markus Tempelmayr2
  1. 1University of Edinburgh, Edinburgh, United Kingdom
  2. 2Universität Münster, Münster, Germany, and EPFL, Lausanne, Switzerland
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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 d≥ 1 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 [GGKO23, Remark 9.1].

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Cite

BibTeXRIS
BibTeX
@article{gvalani2026stochastic,
  title = {{Stochastic Estimates for the Thin-Film Equation with Thermal Noise}},
  author = {Rishabh S. Gvalani and Markus Tempelmayr},
  journal = {Communications in Mathematical Physics},
  year = {2026},
  month = aug,
  doi = {10.1007/s00220-026-05695-1},
  url = {https://doi.org/10.1007/s00220-026-05695-1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Stochastic Estimates for the Thin-Film Equation with Thermal Noise
AU  - Rishabh S. Gvalani
AU  - Markus Tempelmayr
PY  - 2026
DA  - 2026/08/01
JO  - Communications in Mathematical Physics
DO  - 10.1007/s00220-026-05695-1
UR  - https://doi.org/10.1007/s00220-026-05695-1
AB  - 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 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 [GGKO23, Remark 9.1].
SN  - 0010-3616
SN  - 1432-0916
ER  -