Well-posedness of the stochastic thin-film equation with an interface potential
arxiv(2024)
摘要
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 L^p-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 u^n for n∈ [0,6) as long as the
interface potential is sufficiently repulsive.
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