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

TL;DR

This paper proves the soliton resolution conjecture for the radial energy-critical nonlinear heat equation in dimensions three and higher, showing solutions decompose into ground states and radiation over time.

Contribution

It establishes the soliton resolution conjecture for the first time in the radial energy-critical nonlinear heat equation setting in dimensions D≥3.

Findings

Solutions decompose into ground states and radiation asymptotically.

The result holds for all finite energy solutions in the radial case.

The proof confirms the conjecture in the specified setting.

Abstract

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