Adami R.
Blow-Up for Schroedinger Equation with Pointwise
Nonlinearity
(29K, LATeX 2e)
ABSTRACT. We compare classical results on blow-up for the standard
nonlinear Schroedinger equation with some new achievements on the
Schroedinger equation in dimension three with a pointwise nonlinearity. We
show that the pointlike interaction model reproduce the basic features of
the standard NLSE in a simpler and more tractable context.
Finally, we show that the analogy does not hold for the two dimensional
case, whose structure radically differs from the three dimensional one.
In particular, we prove that, in two dimensions,
an arbitrarily small nonlinearity power can actually produce the blow-up
phenomenon.