  We present a detailed numerical study of various blow-up issues in the
context of the focusing Davey-Stewartson II equation. To this end we study
Gaussian initial data and perturbations of the lump and the explicit blow-up
solution due to Ozawa. Based on the numerical results it is conjectured that
the blow-up in all cases is self similar, and that the time dependent scaling
is as in the Ozawa solution and not as in the stable blow-up of standard
$L^{2}$ critical nonlinear Schr\"odinger equations. The blow-up profile is
given by a dynamically rescaled lump.
