Soliton resolution for critical co-rotational wave maps and radial cubic wave equation

2021/03/01 by Thomas Duyckaerts, Carlos Kenig, Yvan Martel +1 · 2 citations
Mathematics · #math.AP

paper · pdf · doi:10.1007/s00220-022-04330-z

arxiv created 2021/03/01 · arxiv updated 2022/02/23

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.

Cited by

• A proof of the soliton resolution conjecture for the Benjamin--Ono equation
• Channels of Energy for the Linearized Energy Critical Wave Equation in Even Dimensions N≥ 8