Existence of nonnegative energy-dissipating solutions to a class of stochastic thin-film equations under weak slippage: Part II -- compactly supported initial data
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909222512361472 |
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| author | Grün, Günther Klein, Lorenz |
| author_facet | Grün, Günther Klein, Lorenz |
| contents | We prove existence of martingale solutions to a class of stochastic thin-film equations for mobility exponents $n \in (2,3)$ and compactly supported initial data. With the perspective to study free-boundary problems related to stochastic thin-film equations in future work, we start from the surface-tension driven stochastic thin-film equation with Stratonovich noise and exploit the regime of coefficients in front of the Stratonovich correction term (which is of porous-media-type) for which energy dissipation can be established. By Bernis inequalities, third order spatial derivatives of appropriate powers of the solution are controlled. Analytically, we rely on approximation with $\mathbb{P}$-almost surely strictly positive solutions and compactness methods based on energy-entropy estimates as well as martingale identification techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of nonnegative energy-dissipating solutions to a class of stochastic thin-film equations under weak slippage: Part II -- compactly supported initial data Grün, Günther Klein, Lorenz Analysis of PDEs 60H15, 76A20, 35G20, 35Q35, 35K65, 35R35, 35R37 We prove existence of martingale solutions to a class of stochastic thin-film equations for mobility exponents $n \in (2,3)$ and compactly supported initial data. With the perspective to study free-boundary problems related to stochastic thin-film equations in future work, we start from the surface-tension driven stochastic thin-film equation with Stratonovich noise and exploit the regime of coefficients in front of the Stratonovich correction term (which is of porous-media-type) for which energy dissipation can be established. By Bernis inequalities, third order spatial derivatives of appropriate powers of the solution are controlled. Analytically, we rely on approximation with $\mathbb{P}$-almost surely strictly positive solutions and compactness methods based on energy-entropy estimates as well as martingale identification techniques. |
| title | Existence of nonnegative energy-dissipating solutions to a class of stochastic thin-film equations under weak slippage: Part II -- compactly supported initial data |
| topic | Analysis of PDEs 60H15, 76A20, 35G20, 35Q35, 35K65, 35R35, 35R37 |
| url | https://arxiv.org/abs/2406.08427 |