| Abstract: |
| We study a one dimensional dynamical system describing viscous fiber stretching, arising from industrial fiber spinning processes in which a highly viscous fluid is drawn into a thin filament. The model is obtained by cross sectional averaging of the axisymmetric Stokes equations with a free boundary and yields a coupled nonlinear evolution for mass transport and momentum balance dominated by viscous forces.\
Using a Lagrangian formulation, we derive a representation of the fiber cross sectional area that ensures forward invariance of positivity, rules out finite time breakup, and allows continuation of local solutions to global ones, yielding existence and uniqueness of the induced semiflow.\
The presentation addresses extensions to nonisothermal models, where temperature dependent viscosity couples the dynamics to a temperature equation and introduces a moving boundary formulation. We highlight which elements of the Lagrangian approach continue to govern global evolution and which require modification due to thermal coupling and boundary motion. |
|