Solutions To The Stochastic Thin-Film Equation For Initial Values With Non-Full Support
Konstantinos Dareiotis (University of Leeds)
Benjamin Gess (Bielefeld University, Max Planck Institute for Mathematics in the Sciences)
M.V. Gnann (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M. Sauerbrey (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
The stochastic thin-film equation with mobility exponent (Formula presented), 3q on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on existing results in three aspects: (1) Non-quadratic mobility with not necessarily strictly positive initial data, (2) Measure-valued initial data, (3) Less spatial regularity of the noise. This is achieved by carrying out a compactness argument based solely on the control of the α-entropy dissipation and the conservation of mass.