  We study the problem of evaporating drops contracting to a point. Going back
to Maxwell and Langmuir, the existence of a spherical solution for which
evaporating drops collapse to a point in a self-similar manner is well
established in the physical literature. The diameter of the drop follows the
so-called $D^{2}$ law: the second power of the drop-diameter decays linearly in
time. In this study we provide a complete mathematical proof of this classical
law. We prove that evaporating drops which are initially small perturbations of
a sphere collapse to a point and the shape of the drop converges to a
self-similar ellipsoid whose center, orientation, and semi-axes are determined
by the initial shape.
