Continuous in time bubbling and Soliton Resolution for Non-negative Solutions of the Energy-Critical Heat Flow
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911349653635072 |
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| author | Aryan, Shrey |
| author_facet | Aryan, Shrey |
| contents | We show that any finite energy solution of the energy-critical nonlinear heat flow in dimensions $d\geq 3$ asymptotically resolves into a sum of possibly time-dependent solitons, a radiation term, and an error term that vanishes in the energy space. As a consequence, when the initial data has finite energy and is non-negative, we settle the Soliton Resolution Conjecture for all dimensions $d\geq 3.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous in time bubbling and Soliton Resolution for Non-negative Solutions of the Energy-Critical Heat Flow Aryan, Shrey Analysis of PDEs We show that any finite energy solution of the energy-critical nonlinear heat flow in dimensions $d\geq 3$ asymptotically resolves into a sum of possibly time-dependent solitons, a radiation term, and an error term that vanishes in the energy space. As a consequence, when the initial data has finite energy and is non-negative, we settle the Soliton Resolution Conjecture for all dimensions $d\geq 3.$ |
| title | Continuous in time bubbling and Soliton Resolution for Non-negative Solutions of the Energy-Critical Heat Flow |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.18840 |