scholarly journals The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge

1981 ◽  
Vol 82 (1) ◽  
pp. 1-28 ◽  
Author(s):  
J. Ginibre ◽  
G. Velo
Keyword(s):  
Cauchy Problem ◽  
Scalar Fields ◽  
Yang Mills ◽  
Temporal Gauge ◽  
The Cauchy Problem

scholarly journals The Cauchy Problem for Space-Time Monopole Equations in Temporal and Spatial Gauge

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Hyungjin Huh ◽  
Jihyun Yim
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Space Dimension ◽  
Space Time ◽  
Gauge Condition ◽  
Existence Of Solution ◽  
Temporal Gauge ◽  
The Cauchy Problem ◽  
Temporal And Spatial ◽  
One Space Dimension

We prove global existence of solution to space-time monopole equations in one space dimension under the spatial gauge condition A1=0 and the temporal gauge condition A0=0.

scholarly journals THE CAUCHY PROBLEM FOR f(R)-GRAVITY: AN OVERVIEW

2012 ◽  
Vol 09 (01) ◽  
pp. 1250006 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
S. VIGNOLO
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
Scalar Fields ◽  
Conformal Transformations ◽  
Field Equations ◽  
The Cauchy Problem ◽  
Theories Of Gravity ◽  
Matter Fields

We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine formulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources in the field equations is discussed in view of the well-formulation and the well-position of the problem. Finally, criteria of viability of the f(R)-models are considered according to the various matter fields acting as sources.

scholarly journals Global well-posedness in energy space for the Chern–Simons–Higgs system in temporal gauge

2016 ◽  
Vol 13 (02) ◽  
pp. 331-351 ◽  
Author(s):  
Hartmut Pecher
Keyword(s):  
Cauchy Problem ◽  
Energy Space ◽  
Well Posedness ◽  
Null Condition ◽  
Temporal Gauge ◽  
Time Estimates ◽  
Dimensional Minkowski Space ◽  
The Cauchy Problem ◽  
Chern Simons ◽  
Well Posed

The Cauchy problem for the Chern–Simons–Higgs system in the [Formula: see text]-dimensional Minkowski space in temporal gauge is globally well-posed in energy space improving a result of Huh. The proof uses the bilinear space-time estimates in wave-Sobolev spaces by d’Ancona, Foschi and Selberg, an [Formula: see text]-estimate for solutions of the wave equation, and also takes advantage of a null condition.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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