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

2021/08/12 by Max Sauerbrey, Sauerbrey, Max
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35R60 #76A20 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2108.05754

openalex publication_date 2021/08/12 · openalex created_date 2023/01/13 · openalex updated_date 2026/07/28

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.

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