Martingale solutions to the stochastic thin-film equation in two dimensions

Max Sauerbrey

doi:10.1214/22-AIHP1328

Martingale solutions to the stochastic thin-film equation in two dimensions

Max Sauerbrey^*

^*Corresponding author for this work

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Abstract

We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension d = 2 and allow in particular for solutions with non-full support. The construction relies on a Trotter–Kato time-splitting scheme, which was recently employed in d = 1. The additional analytical challenges due to the higher spatial dimension are overcome using α-entropy estimates and corresponding tightness arguments.

Original language	English
Pages (from-to)	373-412
Number of pages	40
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	60
Issue number	1
DOIs	https://doi.org/10.1214/22-AIHP1328
Publication status	Published - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Noise
Stochastic compactness method
Thin-film equation
α-Entropy estimates

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N2 - We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension d = 2 and allow in particular for solutions with non-full support. The construction relies on a Trotter–Kato time-splitting scheme, which was recently employed in d = 1. The additional analytical challenges due to the higher spatial dimension are overcome using α-entropy estimates and corresponding tightness arguments.

AB - We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension d = 2 and allow in particular for solutions with non-full support. The construction relies on a Trotter–Kato time-splitting scheme, which was recently employed in d = 1. The additional analytical challenges due to the higher spatial dimension are overcome using α-entropy estimates and corresponding tightness arguments.

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KW - Stochastic compactness method

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KW - α-Entropy estimates

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 1

ER -

Martingale solutions to the stochastic thin-film equation in two dimensions

Abstract

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Keywords

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