论文标题
Kolmogorov的随机汉堡方程和随机2D-Navier-Stokes方程的向后方程
The Kolmogorov backward equation for stochastic Burgers equations and for stochastic 2D-Navier-Stokes equations
论文作者
论文摘要
在本书中，我们在适当的假设下建立了Kolmogorov方程的粘度解的独特性和存在，用于随机部分微分方程（SPDES）。此外，我们表明该解决方案是相应SPDE的半群。这将Feynman-KAC公式推广到SPDE，并在Kolmogorov方程的解决方案与相应SPDES的解决方案之间建立联系。与文献相反，我们仅假设漂移的非线性部分是Lipschitz在有限集（而不是全球Lipschitz连续的）上连续的，我们允许扩散系数退化和非恒定恒定。在本书的最后一部分中，我们将结果应用于随机汉堡方程和随机2-D Navier-Stokes方程。
In this book we establish under suitable assumptions the uniqueness and existence of viscosity solutions of Kolmogorov backward equations for stochastic partial differential equations (SPDEs). In addition, we show that this solution is the semigroup of the corresponding SPDE. This generalizes the Feynman-Kac formula to SPDEs and establishes a link between solutions of Kolmogorov equations and solutions of the corresponding SPDEs. In contrast to the literature we only assume that the nonlinear part of the drift is Lipschitz continuous on bounded sets (and not globally Lipschitz continuous) and we allow the diffusion coefficient to be degenerate and non-constant. In the last part of this book we apply our results to stochastic Burgers equations and to stochastic 2-D Navier-Stokes equations.
