Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

  title={Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise},
  author={Konstantinos Dareiotis and Benjamin Gess and Manuel V. Gnann and G{\"u}nther Gr{\"u}n},
  journal={Archive for Rational Mechanics and Analysis},
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… 
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