Abstract
We show that Yang-Mills equation in 3 dimensions is local well-posedness in Hs if the norm is sufficiently. Here, we construct a solution on the quadric that is independent of the time. And we also construct a solution of the polynomial form. In the process of solving, the polynomial is used to solve the problem before solving.
Highlights
Introduction and PreliminariesThis paper is concerned with the solution of the Yang-Mills equation.We shall denote g -valued tensors define on Minkowski space-time Aα : R3+1 → g by bold character Aα, where α ranges over 0, 1, 2, 3
We show that Yang-Mills equation in 3 dimensions is local well-posedness in H s if the norm is sufficiently
The solution of the polynomial form of Yang-Mills equation is expressed in the form of (13)
Summary
This paper is concerned with the solution of the Yang-Mills equation. We shall denote g -valued tensors define on Minkowski space-time Aα : R3+1 → g by bold character Aα , where α ranges over 0, 1, 2, 3. [,] denotes the Lie bracket of g. It appears in calculations whenever we commute covariant derivatives [4] [5], or more precisely that. The Cauchy problem for Yang-mills equation is not well-posed because of gauge invariance (see [6] [7]). If one fixes the connection to lie in the temporal gauge A0 = 0 , the Yang-Mills equations become essentially hyperbolic [8] [9], and simplify to. This paper will show that the solution of operator and polynomial type
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