Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898982 | Journal of Differential Equations | 2018 | 45 Pages |
Abstract
We consider the initial-value problem for the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in RtÃRx2 with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in Hs 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 Up and Vp spaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zhuo Min Lim,