Well-Posedness of the Stochastic Thin-Film Equation with an Interface Potential
Antonio Agresti (Sapienza University of Rome, TU Delft - Electrical Engineering, Mathematics and Computer Science)
Max Sauerbrey (TU Delft - Electrical Engineering, Mathematics and Computer Science, Max Planck Institute for Mathematics in the Sciences)
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Abstract
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. We prove local Lipschitz estimates in Bessel potential spaces under minimal assumptions on the parameters and corresponding stochastic maximal Lp-regularity estimates for thin-film type operators with measurable in time coefficients. As a result, we deduce local well-posedness of the stochastic thin-film equation as well as blow-up criteria and instantaneous regularization for the solution. In dimension one, we additionally close α-entropy estimates and subsequently an energy estimate for the stochastic thin-film equation with an interface potential so that global well-posedness follows. We allow for a wide range of mobility functions, including the power laws un for n∈[0,6) as long as the interface potential is sufficiently repulsive.
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