Soliton resolution for the energy-critical nonlinear Ginzburg-Landau equation in the radial case
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908855204577280 |
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| author | Yin, Yuchen |
| author_facet | Yin, Yuchen |
| contents | We study the the energy critical non-linear Ginzburg-Landau equation $\partial_{t} u =zΔu+z|u|^{\frac{4}{D-2}} u$ with $\Re z >0$ in dimension $D\geq 3$. We prove that every radial solution with finite energy norm resolves into a finite superposition of asymptotically decoupled copies of the ground state and free radiation continuously in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23398 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Soliton resolution for the energy-critical nonlinear Ginzburg-Landau equation in the radial case Yin, Yuchen Analysis of PDEs We study the the energy critical non-linear Ginzburg-Landau equation $\partial_{t} u =zΔu+z|u|^{\frac{4}{D-2}} u$ with $\Re z >0$ in dimension $D\geq 3$. We prove that every radial solution with finite energy norm resolves into a finite superposition of asymptotically decoupled copies of the ground state and free radiation continuously in time. |
| title | Soliton resolution for the energy-critical nonlinear Ginzburg-Landau equation in the radial case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.23398 |