We consider the self-dual Chern-Simons-Schrödinger equations under radial symmetry (or equivariant index m = 0). The radial soliton Q with the least mass has slow spatial decay. Due to this, the blow-up solutions obtained by the pseudoconformal transform of Q have infinite energy. One can naturally ask what happens to blow-up solutions in energy class. In this talk, I will present the construction of blow-up solutions from smooth and localized initial data. It turns out the story goes differently from high equivariant cases (m 1). Also, I will add more discussion on possible blow-up rates. This talk is based on joint works with Kihyun Kim (IHES) and Sung-Jin Oh (UC Berkeley)

 

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