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

DOI10.1214/22-AIHP1328arXiv2108.05754OpenAlexW3187229686MaRDI QIDQ6127302

Max Sauerbrey

Publication date: 12 April 2024

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

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 $alpha$-entropy estimates and corresponding tightness arguments.

Full work available at URL: https://arxiv.org/abs/2108.05754

zbMATH Keywords

noisethin-film equationstochastic compactness method\( \alpha \)-entropy estimates

Mathematics Subject Classification ID

Thin fluid films (76A20) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (1)

Thin film equations with nonlinear deterministic and stochastic perturbations

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