论文标题
与非线性梯度噪声的随机薄膜方程式的非负胸甲解决方案
Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
论文作者
论文摘要
我们证明了一类随机退化促谁形蛋白寄生虫四阶PDE的非负蛋白溶液的存在，该PDE在受热噪声影响的表面驱动薄膜流中产生。该结构适用于一系列动员，包括在液体固定界面处于无滑动条件下发生的立方体。自从15年前引入以来，戴维维奇（Davidovitch），莫罗（Moro）和斯通（Stone）以及格吕恩（Grün），麦克（Mecke）和劳斯（Rauscher）的引入以来，即使在足够规律的噪音的情况下，即使是随机薄膜方程的解决方案也是一个空旷的问题。我们的全球时间解决方案证明依赖于熵和能量估计的仔细组合以及量身定制的近似程序，以控制由噪声的非线性随机标量保护定律结构引起的冲击形成。
We prove the existence of nonnegative 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.
