  We investigate theoretically the onset of capillary-gravity waves created by
a small object moving at the water-air interface. It is well established that,
for straight uniform motion, no steady waves appear at velocities below the
minimum phase velocity $c_\text{min} = 23 {\rm cm/s}$. At higher velocities the
emission of capillary-gravity waves creates an additional drag force. The
behavior of this force near the critical velocity is still poorly understood. A
linear response theory where the object is replaced by an effective pressure
source predicts a singular behavior for the wave drag. However, experimental
data tends to indicate a more continuous transition. In this article, we show
that a proper treatment of the flow equations around the obstacle can
regularize wave emission, even in the linear wave approximation, thereby
ensuring a continuous behavior of the drag force.
