In this talk, I will discuss some recent developments on the long-term dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariantsymmetry. CSS is a gauge-covariant 2D cubic nonlinear Schrödingerequation, which admits the L2-scaling/pseudoconformalinvariance and soliton solutions.I will first discuss soliton resolution for this model, which is a remarkable consequence of the self-duality and non-local nonlinearity that are distinguished features of CSS. Next, I will discuss the blow-up dynamics (singularity formation) for CSS and introduce an interesting instability mechanism (rotational instability) of finite-time blow-up solutions. This talk is based on joint works with SoonsikKwon and Sung-JinOh.
|