Solutions to the stochastic thin-film equation for initial values with non-full support

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  • Authors: Konstantinos Dareiotis, Benjamin Gess, Manuel V. Gnann, Max Sauerbrey
  • Preprint year: 2023
  • First public date: 2023-05-10
  • arXiv: 2305.06017
  • Status: Published
  • Publication type: Journal article
  • Publication year: 2026
  • Journal: Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383
  • DOI: 10.1090/tran/9367

Abstract

The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on existing results in three aspects: (1) Non-quadratic mobility with not necessarily strictly positive initial data, (2) Measure-valued initial data, (3) Less spatial regularity of the noise. This is achieved by carrying out a compactness argument based solely on the control of the $α$-entropy dissipation and the conservation of mass.

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BibTeX

@article{arxiv230506017,
  title = {Solutions to the stochastic thin-film equation for initial values with non-full support},
  author = {Konstantinos Dareiotis and Benjamin Gess and Manuel V. Gnann and Max Sauerbrey},
  year = {2026},
  journal = {Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383},
  doi = {10.1090/tran/9367},
  eprint = {2305.06017},
  archivePrefix = {arXiv},
  primaryClass = {math.AP}
}

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