Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs equations in the Lorenz gauge

DOI10.1080/03605302.2015.1132730zbMath1342.35281arXiv1209.3841OpenAlexW1595927183MaRDI QIDQ2810603

Hyungjin Huh, Sung-Jin Oh

Publication date: 3 June 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.3841

zbMATH Keywords

local well-posednessnull structureChern-Simons-DiracLorenz gaugeChern-Simons-Higgs

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Second-order nonlinear hyperbolic equations (35L70) First-order nonlinear hyperbolic equations (35L60) PDEs in connection with quantum mechanics (35Q40) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (15)

Small data global existence and decay for relativistic Chern-Simons equations ⋮ Local well-posedness of the coupled Yang-Mills and Dirac system in temporal gauge ⋮ Local well-posedness for the Maxwell-Dirac system in temporal gauge ⋮ Unnamed Item ⋮ On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge ⋮ Remarks on Chern-Simons-Dirac equations in one space dimension ⋮ Local well-posedness of non-abelian Chern-Simons-Higgs system in the Lorenz gauge ⋮ Conformal identity of the Chern–Simons gauged wave equations and its applications ⋮ Small data scattering of 2d Hartree type Dirac equations ⋮ Nonexistence of global solution to Chern-Simons-Higgs system ⋮ Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge ⋮ Low regularity well-posedness of Hartree type Dirac equations in 2, 3-dimensions ⋮ Global well-posedness in energy space for the Chern–Simons–Higgs system in temporal gauge ⋮ Low regularity solutions to the non-abelian Chern-Simons-Higgs system in the Lorenz gauge ⋮ Local well-posedness of the coupled Yang–Mills and Dirac system for low regularity data

Cites Work

• Local and global solutions of the Chern-Simons-Higgs system
• Cauchy problem for the Fermion field equation coupled with the Chern-Simons gauge
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Smoothing estimates for null forms and applications
• Global well-posedness of the Chern-Simons-Higgs equations with finite energy
• Towards the Chern-Simons-Higgs equation with finite energy
• Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system
• Global existence in the Cauchy problem of the relativistic Chern-Simons-Higgs theory
• Finite-Energy Global Well-Posedness of the Maxwell–Klein–Gordon System in Lorenz Gauge
• Space‐time estimates for null forms and the local existence theorem
• Local existence with minimal regularity for nonlinear wave equations
• Self-dual Chern-Simons vortices
• Multivortex solutions of the Abelian Chern-Simons-Higgs theory
• Self-Dual Chern-Simons Theories

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