Semi-Discretized Stochastic Fiber Dynamics: Non-Linear Drag Force

Abstract

We analyze a spatially discretized model for the dynamics of a thin, long, elastic, inextensible fiber in a turbulent flow as occurring, e.g., in the spunbond production process of non-woven textiles. It consists of a high-dimensional stochastic differential equation with a non-linear algebraic constraint and an associated Lagrange multiplier term. We prove existence and uniqueness of a global strong solution for the case of a non-linear underlying drag force model. Our result generalizes previous findings which are based on a simplified linear drag force model.