Large Data Well-posedness in the Energy Space of the Chern-Simons-Schrödinger System

2015/12/21 by Lim, Zhuo Min · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.06605

Abstract

We consider the initial-value problem for the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in ℝ_t×ℝ²_x with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in H^s for s≥ 1, and the solution map satisfies a local-in-time weak Lipschitz bound. By energy conservation, we also obtain a global regularity result. The key is to retain the non-perturbative part of the derivative nonlinearity in the principal operator, and exploit the dispersive properties of the resulting paradifferential-type principal operator using adapted U^p and V^p spaces.

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• Dimensional reduction for anyons in the average-field approximation
• Equivariant stability of vortices in Manton's Chern-Simons-Schrödinger system on the hyperbolic plane

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