  The effect of an external pressure disturbance, being displaced with a
constant speed along the free surface of a viscous thin film, is studied
theoretically in the lubrication approximation in one- and two-dimensional
geometries. In the comoving frame, the imposed pressure field creates a
stationary deformation of the interface - a wake - that spatially vanishes in
the far region. The shape of the wake and the way it vanishes depend on both
the speed and size of the external source and the properties of the film. The
wave resistance, namely the force that has to be externally furnished in order
to maintain the wake, is analysed in details. For finite-size pressure
disturbances, it increases with the speed, up to a certain transition value
above which a monotonic decrease occurs. The role of the horizontal extent of
the pressure field is studied as well, revealing that for a smaller disturbance
the latter transition occurs at higher speed. Eventually, for a Dirac pressure
source, the wave resistance either saturates in a 1D geometry, or diverges in a
2D geometry.
