We prove existence of martingale solutions to a class of stochastic thin-film equations for mobility exponents \(n \in (2,3)\) and compactly supported initial data. With the perspective to study free-boundary problems related to stochastic thin-film equations in Grün and Klein (SIAM J Math Anal), we start from the surface-tension driven stochastic thin-film equation with Stratonovich noise and exploit the regime of coefficients in front of the Stratonovich correction term (which—under natural assumptions on the spatially colored noise—is of porous-media-type) for which energy dissipation can be established. By Bernis inequalities, third order spatial derivatives of appropriate powers of the solution are controlled. Analytically, we rely on approximation with \({\mathbb {P}}\) -almost surely strictly positive solutions and compactness methods based on energy-entropy estimates as well as martingale identification techniques.
