On Threshold Solutions of equivariant Chern-Simons-Schrödinger Equation

Abstract

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

arXiv comment40 pages

References in corpus (9)

• Self-Dual Chern-Simons Theories
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Two-bubble dynamics for threshold solutions to the wave maps equation
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Equivariant Schrödinger Maps in two spatial dimensions
• Global wellposedness of the equivariant Chern-Simons-Schrödinger equation
• Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions
• On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability
• Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schrödinger equation