Title: A New Non-Linear Density Fluctuations Stochastic Partial Differential Equation With a Singular Coefficient of Relevance to Polymer Dynamics and Rheology: Discussions, Proofs of Solution Existence, Uniqueness, and a Conjecture Show Chinese title

Title: 关于与聚合物动力学和流变学相关的具有奇异系数的新非线性密度涨落随机偏微分方程：讨论、解的存在性和唯一性证明以及一个猜想

Abstract: In this paper we consider an entirely new - previously unstudied to the best of our knowledge - type of density fluctuations stochastic partial differential equation with a singular coefficient involving the inverse of a probability density. The equation was recently introduced by Schieber \cite{jay3} while working on a new polymer molecular dynamics approach that pertains to the generally called polymer reptation (aka tube) theory. The corresponding probability density is the solution of an evolution equation (a stochastic transport) defined on a dynamical one-dimensional subspace. A peculiarity of the here studied equation is its very singular pattern, even though it exhibits a well-posed structure. As a first step towards furthering the understanding of this new clas Show Chinese abstract

Abstract: 本文我们考虑了一种全新的——据我们所知此前未被研究过的——带有奇异系数（涉及概率密度的倒数）的密度涨落随机偏微分方程类型。 该方程最近由施比尔 \cite{jay3} 在研究一种新的聚合物分子动力学方法时提出，该方法与通常所说的聚合物爬杆（俗称管状）理论相关。 对应的概率密度是定义在一个动态一维子空间上的演化方程（随机输运）的解。 这里所研究方程的一个特点是其非常奇异的形式，尽管它具有适定的结构。 作为进一步理解这一新类别的第一步，