Well-posedness of the stochastic thin-film equation with an interface potential

We consider strictly positive solutions to a class of fourth-order conservative quasilinear SPDEs on the d-dimensional torus modeled after the stochastic thin-film equation. Using recent results on quasilinear stochastic evolution equations, we show local well-posedness, blow-up criteria and instantaneous regularization in suitable function spaces under corresponding smoothness conditions on the noise. As a key ingredient, we prove stochastic maximal Lᵖ-regularity estimates for thin film-type operators with measurable in time coefficients. With the aid of the above-mentioned results, we obtain global well-posedness of the stochastic thin-film equation with an interface potential by closing α-entropy estimates and subsequently an energy estimate in dimension one. In particular, we can treat a wide range of mobility functions including the power laws uⁿ for n∈ [0,6) as long as the interface potential is sufficiently repulsive.