Well-posedness for the dimension-reduced Chern–Simons–Dirac system

2016 ◽  
Vol 17 (3) ◽  
pp. 1031-1048 ◽  
Author(s):  
Shuji Machihara ◽  
Mamoru Okamoto
Keyword(s):  
Well Posedness ◽  
Dirac System ◽  
Chern Simons

WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN–SIMONS–DIRAC SYSTEM IN TWO DIMENSIONS

2013 ◽  
Vol 10 (04) ◽  
pp. 735-771 ◽  
Author(s):  
MAMORU OKAMOTO
Keyword(s):  
Cauchy Problem ◽  
Dirac Equation ◽  
Sobolev Space ◽  
Gauge Invariance ◽  
Two Dimensions ◽  
Well Posedness ◽  
Dirac System ◽  
The Cauchy Problem ◽  
Chern Simons ◽  
Well Posed

We consider the Cauchy problem associated with the Chern–Simons–Dirac system in ℝ1+2. Using gauge invariance, we reduce the Chern–Simons–Dirac system to a Dirac equation and we uncover the null structure of this Dirac equation. Next, relying on null structure estimates, we establish that the Cauchy problem associated with this Dirac equation is locally-in-time well-posed in the Sobolev space Hs for all s > 1/4. Our proof uses modified L4-type estimates.

scholarly journals Global well-posedness of the Chern-Simons-Higgs equations with finite energy

2013 ◽  
Vol 33 (6) ◽  
pp. 2531-2546 ◽  
Author(s):  
Sigmund Selberg ◽  
◽  
Achenef Tesfahun
Keyword(s):  
Finite Energy ◽  
Well Posedness ◽  
Chern Simons

Null structure and almost optimal local well-posedness of the Maxwell-Dirac system

2010 ◽  
Vol 132 (3) ◽  
pp. 771-839 ◽  
Author(s):  
Piero D'Ancona ◽  
Damiano Foschi ◽  
Sigmund Selberg
Keyword(s):  
Well Posedness ◽  
Dirac System

Corrigendum: Local well-posedness of the coupled Yang–Mills and Dirac system for low regularity data (2022 Nonlinearity 35 1)

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. C3-C4
Author(s):  
Hartmut Pecher
Keyword(s):  
Well Posedness ◽  
Dirac System ◽  
Low Regularity ◽  
Yang Mills

Abstract An error in the proof of the main theorem is fixed.

scholarly journals Local well-posedness of the coupled Yang–Mills and Dirac system for low regularity data

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 1-29
Author(s):  
Hartmut Pecher
Keyword(s):  
Dirac Equation ◽  
Well Posedness ◽  
Dirac System ◽  
Null Condition ◽  
Low Regularity ◽  
Yang Mills ◽  
Smooth Data

Abstract We consider the classical Yang–Mills system coupled with a Dirac equation in 3 + 1 dimensions. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Choquet-Bruhat and Christodoulou. Our result generalises a similar result for the Yang–Mills equation by Selberg and Tesfahun.

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