×

Local well-posedness of Chern-Simons-Higgs system in the Lorentz gauge. (English) Zbl 1272.81216

Summary: In this paper, we investigate the local well-posedness of the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge. By exploiting the null structure in the nonlinear terms of the equations, we reprove the low regularity result by N. Bournaveas [Electron. J. Differ. Equ. 2009, Paper No. 114, 10 p., electronic only (2009; Zbl 1178.35258)].{
©2011 American Institute of Physics}

MSC:

81V22 Unified quantum theories
58J28 Eta-invariants, Chern-Simons invariants
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
35Q55 NLS equations (nonlinear Schrödinger equations)
82D55 Statistical mechanics of superconductors

Citations:

Zbl 1178.35258
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bournaveas N., Electron. J. Differ. Equ. 2009 (114) pp 1–
[2] DOI: 10.1088/0951-7715/15/3/314 · Zbl 1073.58014
[3] DOI: 10.4171/JEMS/100 · Zbl 1187.35191
[4] D’Ancona P., Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena pp 125– (2010)
[5] DOI: 10.1007/BF01206943 · Zbl 0486.35048
[6] DOI: 10.1103/PhysRevLett.64.2230 · Zbl 1014.58500
[7] DOI: 10.1088/0951-7715/18/6/009 · Zbl 1080.35041
[8] DOI: 10.1016/j.jfa.2006.09.009 · Zbl 1246.58009
[9] DOI: 10.1103/PhysRevLett.64.2234 · Zbl 1050.81595
[10] DOI: 10.1142/S0219199702000634 · Zbl 1146.35389
[11] DOI: 10.1080/03605301003717100 · Zbl 1193.35164
[12] DOI: 10.1353/ajm.1997.0020 · Zbl 0881.35077
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.