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We construct solutions to the stochastic thin-film equation with quadraticmobility and Stratonovich gradient noise in the physically relevant dimension$d=2$ and allow in particular for solutions with non-full support. Theconstruction relies on a Trotter-Kato time-splitting scheme, which was recentlyemployed in $d=1$. The additional analytical challenges due to the higherspatial dimension are overcome using $\alpha$-entropy estimates andcorresponding tightness arguments.

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