Stochastic estimates for the thin-film equation with thermal noise
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917506661220352 |
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| author | Gvalani, Rishabh S. Tempelmayr, Markus |
| author_facet | Gvalani, Rishabh S. Tempelmayr, Markus |
| contents | We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension $d\geq 1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15829 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic estimates for the thin-film equation with thermal noise Gvalani, Rishabh S. Tempelmayr, Markus Analysis of PDEs Mathematical Physics Probability 60H17, 60L30 We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension $d\geq 1$ 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. |
| title | Stochastic estimates for the thin-film equation with thermal noise |
| topic | Analysis of PDEs Mathematical Physics Probability 60H17, 60L30 |
| url | https://arxiv.org/abs/2309.15829 |