Dareiotis K, Gess B, Gnann M, Grün G (2021)
Publication Type: Journal article
Publication year: 2021
DOI: 10.1007/s00205-021-01682-z
We prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise.
APA:
Dareiotis, K., Gess, B., Gnann, M., & Grün, G. (2021). Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise. Archive for Rational Mechanics and Analysis. https://doi.org/10.1007/s00205-021-01682-z
MLA:
Dareiotis, Konstantinos, et al. "Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise." Archive for Rational Mechanics and Analysis (2021).
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