Well-posedness of the stochastic thin-film equation with an interface potential

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  • Authors: Antonio Agresti, Max Sauerbrey
  • First public date: 2024-03-19
  • arXiv: 2403.12652
  • Preprint year: 2024
  • Status: Published
  • Publication type: Journal article
  • Publication year: 2026
  • Published online: 2026-07-09
  • Journal: Communications in Mathematical Physics 407, 158 (2026)
  • DOI: 10.1007/s00220-026-05563-y

Abstract

We consider strictly positive solutions to a class of fourth-order conservative quasilinear SPDEs on the $d$-dimensional torus modeled after the stochastic thin-film equation. We prove local Lipschitz estimates in Bessel potential spaces under minimal assumptions on the parameters and corresponding stochastic maximal $L^p$-regularity estimates for thin-film type operators with measurable in-time coefficients. As a result, we deduce local well-posedness of the stochastic thin-film equation as well as blow-up criteria and instantaneous regularization for the solution. In dimension one, we additionally close $α$-entropy estimates and subsequently an energy estimate for the stochastic thin-film equation with an interface potential so that global well-posedness follows. We allow for a wide range of mobility functions including the power laws $u^n$ for $n\in [0,6)$ as long as the interface potential is sufficiently repulsive.

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BibTeX

@article{arxiv240312652,
  title = {Well-posedness of the stochastic thin-film equation with an interface potential},
  author = {Antonio Agresti and Max Sauerbrey},
  year = {2026},
  journal = {Communications in Mathematical Physics 407, 158 (2026)},
  doi = {10.1007/s00220-026-05563-y},
  eprint = {2403.12652},
  archivePrefix = {arXiv},
  primaryClass = {math.AP}
}

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