Collapse of Chern-Simons gauged matter fields

Time-dependent solutions of the planar, Chern-Simons gauged nonlinear Schrödinger equation are proved to collapse in a finite time for certain initial data including, e.g., a negative energy. Radially symmetric collapsing structures are found to blow up with a twice-logarithmic contraction rate and to self-focus with a central core whose extension is bounded in space. Finally, interaction of Chern-Simons vortices with an external magnetic field is shown to shorten the collapse time.