Geodesic
On threshold solutions of the equivariant Chern–Simons–Schrödinger equation
Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 2, pp. 371-417

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We consider the self-dual Chern–Simons–Schrödinger model in two spatial dimensions. This problem is L 2 -critical. Under the equivariant setting, global well-posedness and scattering were proved in Liu and Smith (2016) for a solution with initial charge below a certain threshold given by the ground state. In this work, we show that the only nonscattering solutions with threshold charge are exactly the ground state up to scaling, phase rotation and the pseudoconformal transformation. We also obtain a partial result for the non-self-dual system.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/10
Classification : 35Q55
Keywords: Chern–Simons–Schrödinger equation, self-duality, minimal blowup solutions 
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     title = {On threshold solutions of the equivariant {Chern{\textendash}Simons{\textendash}Schr\"odinger} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {371--417},
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     doi = {10.4171/aihpc/10},
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Li, Zexing; Liu, Baoping. On threshold solutions of the equivariant Chern–Simons–Schrödinger equation. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 2, pp. 371-417. doi: 10.4171/aihpc/10

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