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.