Martingale solutions to the stochastic thin-film equation in two dimensions
M. Sauerbrey (TU Delft - Analysis)
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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.