Soliton resolution for critical co-rotational wave maps and radial cubic wave equation
arXiv:2103.01293 · doi:10.1007/s00220-022-04330-z
Abstract
In this paper we prove the soliton resolution conjecture for all times, for all solutions in the energy space, of the co-rotational wave map equation. To our knowledge this is the first such result for all initial data in the energy space for a wave-type equation. We also prove the corresponding results for radial solutions, which remain bounded in the energy norm, of the cubic (energy-critical) nonlinear wave equation in space dimension 4.
References in corpus (19)
- Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
- Regularity of Wave-Maps in dimension 2+1
- Renormalization and blow up for charge one equivariant critical wave maps
- Energy dispersed large data wave maps in 2+1 dimensions
- Two-bubble dynamics for threshold solutions to the wave maps equation
- Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
- Maximizers for the Strichartz Inequalities for the Wave Equation
- Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
- Exterior energy bounds for the critical wave equation close to the ground state
- Universality of blow up profile for small blow up solutions to the energy critical wave map equation
- Inelasticity of soliton collisions for the 5D energy critical wave equation
- Decay estimates for nonradiative solutions of the energy-critical focusing wave equation
- Quantization of time-like energy for wave maps into spheres
- Threshold dynamics for corotational wave maps
- Soliton resolution for the radial critical wave equation in all odd space dimensions
- Uniqueness of two-bubble wave maps
- Continuous time soliton resolution for two-bubble equivariant wave maps
- Infinite time blow-up solutions to the energy critical wave maps equation
- Global, Non-scattering solutions to the energy critical wave maps equation