Advances in Differential Equations

Instability of infinitely-many stationary solutions of the $SU(2)$ Yang-Mills fields on the exterior of the Schwarzschild black hole

Cécile Huneau and Dietrich Häfner

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Abstract

We consider the spherically symmetric $SU(2)$ Yang-Mills fields on the Schwarzschild metric. Within the so called purely magnetic Ansatz, we show that there exists a countable number of stationary solutions which are all nonlinearly unstable.

Article information

Source
Adv. Differential Equations, Volume 24, Number 7/8 (2019), 435-464.

Dates
First available in Project Euclid: 2 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.ade/1556762455

Mathematical Reviews number (MathSciNet)
MR3945768

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations 53C50: Lorentz manifolds, manifolds with indefinite metrics 53C80: Applications to physics 58J45: Hyperbolic equations [See also 35Lxx] 83C57: Black holes

Citation

Häfner, Dietrich; Huneau, Cécile. Instability of infinitely-many stationary solutions of the $SU(2)$ Yang-Mills fields on the exterior of the Schwarzschild black hole. Adv. Differential Equations 24 (2019), no. 7/8, 435--464. https://projecteuclid.org/euclid.ade/1556762455


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