Soliton resolution for the energy-critical nonlinear heat equation in the radial case

Abstract

We establish the Soliton Resolution Conjecture for the radial critical non-linear heat equation in dimension $D\ge 3.$ Thus, every finite energy solution resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.

37 Pages, to appear in Analysis & PDE. arXiv admin note: text overlap with arXiv:2210.14963 by other authors