The threshold theorem for the $(4+1)$-dimensional Yang–Mills equation: An overview of the proof
From MaRDI portal
Publication:4631425
DOI10.1090/bull/1640zbMath1420.35273arXiv1709.09088OpenAlexW2964142702MaRDI QIDQ4631425
Publication date: 29 March 2019
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1709.09088
Scattering theory for PDEs (35P25) Second-order nonlinear hyperbolic equations (35L70) Yang-Mills and other gauge theories in quantum field theory (81T13) PDEs in connection with quantum mechanics (35Q40) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Blow-up in context of PDEs (35B44)
Related Items (9)
On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps ⋮ Stable blowup for the supercritical hyperbolic Yang-Mills equations ⋮ A Globally Stable Self-Similar Blowup Profile in Energy Supercritical Yang-Mills Theory ⋮ The Yang-Mills heat flow with random distributional initial data ⋮ The hyperbolic Yang-Mills equation in the caloric gauge: local well-posedness and control of energy-dispersed solutions ⋮ A state space for 3D Euclidean Yang-Mills theories ⋮ The hyperbolic Yang-Mills equation for connections in an arbitrary topological class ⋮ The threshold conjecture for the energy critical hyperbolic Yang-Mills equation ⋮ Global, non-scattering solutions to the energy critical Yang–Mills problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A refined threshold theorem for \((1+2)\)-dimensional wave maps into surfaces
- Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation
- Concentration compactness for critical wave maps
- Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
- Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
- Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge
- Global regularity for the Maxwell-Klein-Gordon equation with small critical Sobolev norm in high dimensions
- Energy dispersed large data wave maps in \(2+1\) dimensions
- Regularity of wave-maps in dimension \(2+1\)
- Renormalization and blow up for the critical Yang-Mills problem
- The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties
- The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. II. Completion of proof
- Connections with \(L^ p \)bounds on curvature
- Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity
- Regularity results for nonlinear wave equations
- The Yang-Mills flow in four dimensions
- On the Maxwell-Klein-Gordon equation with finite energy
- Long-time behaviour of the Yang-Mills flow in four dimensions
- Concentration compactness for the critical Maxwell-Klein-Gordon equation
- Local well-posedness of the \((4 + 1)\)-dimensional Maxwell-Klein-Gordon equation at energy regularity
- Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\)
- Global well-posedness for the Maxwell-Klein-Gordon equation in \(4+1\) dimensions: small energy
- Finite energy global well-posedness of the Yang-Mills equations on \(\mathbb{R}^{1+3}\): an approach using the Yang-Mills heat flow
- Global well-posedness for the Yang-Mills equation in \(4+1\) dimensions. Small energy.
- On global existence and scattering for the wave maps equation
- Solutions to Yang—Mills equations that are not self-dual
- Regularity for the wave equation with a critical nonlinearity
- On the optimal local regularity for the Yang-Mills equations in ℝ⁴⁺¹
- Space‐time estimates for null forms and the local existence theorem
- Almost optimal local well-posedness for the (3+1)-dimensional Maxwell–Klein–Gordon equations
- Rough solutions for the wave maps equation
- Global regularity for the Yang–Mills equations on high dimensional Minkowski space
- Energy dispersed solutions for the (4 + 1)-dimensional Maxwell-Klein-Gordon equation
- GAUGE CHOICE FOR THE YANG–MILLS EQUATIONS USING THE YANG–MILLS HEAT FLOW AND LOCAL WELL-POSEDNESS IN H1
- Variational Methods
- Removable singularities in Yang-Mills fields
- Global regularity of wave maps. II: Small energy in two dimensions
This page was built for publication: The threshold theorem for the $(4+1)$-dimensional Yang–Mills equation: An overview of the proof
