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

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.

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Bibliographic Details
Published in:arXiv.org 2024-05
Main Author: Shrey Aryan
Format: Article
Language:English
Subjects:
Solitary waves
Thermodynamics
Online Access:Get full text
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Summary: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.
ISSN:2331-8422