Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system

Abstract

We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetric Yang-Mills equation, in the critical energy space, with data of energy smaller than or equal to a harmonic map of minimal energy. An alternative holds: either the data is the harmonic map and the soltuion is constant in time, or the solution scatters in infinite time.

References in corpus (1)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case

Cited by in corpus (10)

• Soliton resolution for critical co-rotational wave maps and radial cubic wave equation
• Universality of blow up profile for small blow up solutions to the energy critical wave map equation
• A globally stable self-similar blowup profile in energy supercritical Yang-Mills theory
• Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications
• Optimal blowup stability for three-dimensional wave maps
• Sharp universal rate for stable blow-up of corotational wave maps
• Renormalization and blow up for wave maps from $S^2\times \RR$ to $S^2$
• Quantized slow blow-up dynamics for the energy-critical corotational wave maps problem
• Optimal polynomial blow up range for critical wave maps
• Renormalization and blow up for the critical Yang-Mills problem