  To investigate the influence of inertia and slip on the instability of a
liquid film on a fibre, a theoretical framework based on the axisymmetric
Navier-Stokes equations is proposed via linear instability analysis. The model
reveals that slip significantly enhances perturbation growth in viscous film
flows, whereas it exerts minimal influence on flows dominated by inertia.
Moreover, under no-slip boundary conditions, the dominant instability mode of
thin films remains unaltered by inertia, closely aligning with predictions from
a no-slip lubrication model. Conversely, when slip is introduced, the dominant
wavenumber experiences a noticeable reduction as inertia decreases. This trend
is captured by an introduced lubrication model with giant slip. Direct
numerical simulations of the Navier-Stokes equations are then performed to
further confirm the theoretical findings at the linear stage. For the nonlinear
dynamics, no-slip simulations show complex vortical structures within films,
driven by fluid inertia near surfaces. Additionally, in scenarios with weak
inertia, a reduction in the volume of satellite droplets is observed due to
slip, following a power-law relationship.
