Soliton Resolution for Critical Co-rotational Wave Maps and Radial Cubic Wave Equation

By Thomas Duyckaerts, Carlos E. Kenig, Yvan Martel, F. Merle. Communications in Mathematical Physics, 2021

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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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f35b97d037ee9648704842d3f22d1d0fc124db9a