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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2504.05911 |
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| _version_ | 1866908306987024384 |
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| author | Liu, Jie |
| author_facet | Liu, Jie |
| contents | In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under Lorentz transformations in self-similar variables. This observation serves as a useful tool in proving mode stability and provides insights that may aid the study of self-similar solutions in related problems. As a direct consequence, we establish the asymptotic stability of the ODE blow-up family, extending the classical results of Merle and Zaag [Merle-Zaag, 2007, 2016] to the superconformal case and generalizing the recent findings of Ostermann [Ostermann, 2024] to include the entire ODE blow-up family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the stability of self-similar blow-up solutions for superconformal semilinear wave equations Liu, Jie Analysis of PDEs In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under Lorentz transformations in self-similar variables. This observation serves as a useful tool in proving mode stability and provides insights that may aid the study of self-similar solutions in related problems. As a direct consequence, we establish the asymptotic stability of the ODE blow-up family, extending the classical results of Merle and Zaag [Merle-Zaag, 2007, 2016] to the superconformal case and generalizing the recent findings of Ostermann [Ostermann, 2024] to include the entire ODE blow-up family. |
| title | A note on the stability of self-similar blow-up solutions for superconformal semilinear wave equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.05911 |