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 (2)

• Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications
• Renormalization and blow up for the critical Yang-Mills problem