scholarly journals Null structure and local well-posedness in the energy class for the Yang–Mills equations in Lorenz gauge

2016 ◽  
Vol 18 (8) ◽  
pp. 1729-1752 ◽  
Author(s):  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Energy Class ◽  
Well Posedness ◽  
Yang Mills ◽  
Lorenz Gauge

scholarly journals Almost critical local well-posedness for the space-time monopole equation in Lorenz gauge

2015 ◽  
Vol 17 (03) ◽  
pp. 1450043 ◽  
Author(s):  
Achenef Tesfahun
Keyword(s):  
Initial Data ◽  
Critical Exponent ◽  
Sobolev Spaces ◽  
Lebesgue Space ◽  
Space Time ◽  
Well Posedness ◽  
Critical Space ◽  
Lorenz Gauge

Recently, Candy and Bournaveas proved local well-posedness of the space-time monopole equation in Lorenz gauge for initial data in Hs with [Formula: see text]. The equation is L2-critical, and hence a [Formula: see text] derivative gap is left between their result and the scaling prediction. In this paper, we consider initial data in the Fourier–Lebesgue space [Formula: see text] for 1 < p ≤ 2 which coincides with Hs when p = 2 but scales like lower regularity Sobolev spaces for 1 < p < 2. In particular, we will see that as p → 1+, the critical exponent [Formula: see text], in which case [Formula: see text] is the critical space. We shall prove almost optimal local well-posedness to the space-time monopole equation in Lorenz gauge with initial data in the aforementioned spaces that correspond to p close to 1.

scholarly journals WELL-POSEDNESS FOR THE MASSIVE WAVE EQUATION ON ASYMPTOTICALLY ANTI-DE SITTER SPACETIMES

2012 ◽  
Vol 09 (02) ◽  
pp. 239-261 ◽  
Author(s):  
GUSTAV HOLZEGEL
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Class ◽  
Well Posedness ◽  
De Sitter ◽  
Initial Boundary Value

In this paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner–Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class (but non-unique if the decay at infinity is weakened).

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.

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