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In this paper we consider an entirely new - previously unstudied to the bestof our knowledge - type of density fluctuations stochastic partial differentialequation with a singular coefficient involving the inverse of a probabilitydensity. The equation was recently introduced by Schieber \cite{jay3} whileworking on a new polymer molecular dynamics approach that pertains to thegenerally called polymer reptation (aka tube) theory. The correspondingprobability density is the solution of an evolution equation (a stochastictransport) defined on a dynamical one-dimensional subspace. A peculiarity ofthe here studied equation is its very singular pattern, even though it exhibitsa well-posed structure. As a first step towards furthering the understanding ofthis new clas

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