Blowing up time-dependent solutions of the planar, Chern-Simons gauged nonlinear Schrodinger equation

Time-dependent solutions of the two-dimensional Chern-Simons gauged nonlinear Schrodinger equation are investigated in terms of an initial-value problem. We prove that this Cauchy problem is locally well posed in H2(R2) that global solutions exist in H1(R2) provided that the initial data are small enough in L2(R2). On the other hand, under certain conditions ensuring, for example a negative Hamiltonian, solutions blow up in a finite time which only depends on the initial data. The diverging shape of collapsing structures is finally discussed throughout a self-similar analysis.