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.

scholarly journals LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION

2008 ◽  
Vol 10 (02) ◽  
pp. 181-194 ◽  
Author(s):  
SIGMUND SELBERG ◽  
ACHENEF TESFAHUN
Keyword(s):  
Dirac Operator ◽  
Space Dimension ◽  
One Dimension ◽  
Well Posedness ◽  
Low Regularity ◽  
Klein Gordon ◽  
One Space Dimension

We extend recent results of Machihara and Pecher on low regularity well-posedness of the Dirac–Klein–Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain–Klainerman–Machedon spaces.

scholarly journals Well posedness for the Kawahara equation on the half-line

2020 ◽  
Author(s):  
Boling Guo ◽  
fengxia liu
Keyword(s):  
Initial Data ◽  
Local Existence ◽  
Half Line ◽  
Well Posedness ◽  
Kawahara Equation ◽  
Low Regularity ◽  
Regularity Properties

We study the low-regularity properties of the Kawahara equation on the half line. We obtain the local existence, uniqueness, and continuity of the solution. Moreover, We obtain that the nonlinear terms of the solution are smoother than the initial data.

Sign in / Sign up

Export Citation Format

Share Document