Research onstochastic partial differential equationswith some singularities

在这个项目中，我主要研究了具有不同奇性的随机偏微分方程解的基本问题、爆炸性和遍历性。特别地，我发现适当的噪声可以延迟一类非线性随机偏微分方程解的爆破时间，导出了著名的带有Levy时间噪声的随机微分方程解的Bismut-Elworth公式。此外，作为联合工作，我们通过对二维进化Young图涨落的研究，导出了一些新的随机偏微分方程组。

In this project, I mainly did some researches on fundamental problems, explosion and ergodicity for stochastic partial differential equations with different singularities. In particular, I found that appropriate noise can delay the blow-up time of a nonlinear stochastic partial differential equation, deduced the well-knows Bismut-Elworthy formula for stochastic differential equations with Levy time noise. Moreover, as joint work, we deduced some new stochastic partial differential equations by the study of the fluctuation of two dimensional evolutionary Young diagrams.