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<p>We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d\ge 1 \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> 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 [<CitationRef CitationID="CR24">GGKO23</CitationRef>, Remark 9.1].</p>

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Stochastic Estimates for the Thin-Film Equation with Thermal Noise

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  • 出版模式：

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  • 发表日期：

    2026年8月1日

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  • Rishabh S. Gvalani,
  • Markus Tempelmayr

摘要

We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension \(d\ge 1 \) 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].