This is the first part of the four-paper sequence, which establishes the Threshold Conjecture and the Soliton Bubbling vs. Scattering Dichotomy for the energy critical hyperbolic Yang-Mills equation in the (4 + 1)-dimensional Minkowski space-time.

The primary subject of this paper, however, is another PDE, namely the energy critical Yang-Mills heat flow on the 4-dimen- sional Euclidean space. Our first goal is to establish sharp criteria for global existence and asymptotic convergence to a flat connection for this system in Ḣ¹, including the Dichotomy Theorem (i.e., either the above properties hold or a harmonic Yang-Mills connection bubbles off) and the Threshold Theorem (i.e., if the initial energy is less than twice that of the ground state, then the above properties hold). Our second goal is to use the Yang-Mills heat flow in order to define the caloric gauge, which will play a major role in the analysis of the hyperbolic Yang-Mills equation in the subsequent papers.

Fiche Technique

Paru le : 18/11/2022

Thématique : Physique générale

Auteur(s) : Auteur : Sung-Jin Oh Auteur : Daniel Tataru

Éditeur(s) : Société mathématique de France

Collection(s) : Non précisé.

Série(s) : Non précisé.

ISBN : 978-2-85629-961-6

EAN13 : 9782856299616

Reliure : Broché

Pages : 128

Hauteur: 24.0 cm / Largeur 18.0 cm

Épaisseur: 1.0 cm

Poids: 0 g