  Reduced one-dimensional equations for the stationary, isothermal rotational
spinning process of slender fibers are considered for the case of large
Reynolds ($\delta=3/\text{Re}\ll 1$) and small Rossby numbers ($\varepsilon \ll
1$). Surface tension is included in the model using the parameter
$\kappa=\sqrt{\pi}/(2 \text{We})$ related to the inverse Weber number. The
inviscid case $\delta=0$ is discussed as a reference case. For the viscous case
$\delta > 0$ numerical simulations indicate, that for a certain parameter
range, no physically relevant solution may exist. Transferring properties of
the inviscid limit to the viscous case, analytical bounds for the initial
viscous stress of the fiber are obtained. A good agreement with the numerical
results is found. These bounds give strong evidence, that for $\delta >
3\varepsilon^2 \left( 1- \frac{3}{2}\kappa +\frac{1}{2}\kappa^2\right)$ no
physical relevant stationary solution can exist.
