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

Journal article (2024)

Authors

M. Sauerbrey Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2024 M. Sauerbrey
DOI: https://doi.org/10.1214/22-AIHP1328
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Published Date

2024

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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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