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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.16079 |
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| _version_ | 1866912801339998208 |
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| author | Higaki, Mitsuo |
| author_facet | Higaki, Mitsuo |
| contents | We establish the first quantitative Runge approximation theorem, with explicit $L^2$-estimates, for the 3d nonstationary Stokes system on a bounded spatial domain. This result addresses the two primary limitations of the qualitative result [H.-Sueur, 2025] obtained in collaboration with Franck Sueur: first, it bypasses the non-constructive Hahn-Banach theorem used in [H.-Sueur, 2025], precluding quantitative estimates; and second, it extends the scope of the theory from interior approximations to the physically important initial-boundary value problem. Our proof is founded on the modern quantitative framework of [Rüland-Salo, 2019], which we adapt to the Stokes system by combining semigroup theory with a quantitative approximation for the associated resolvent problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An $L^2$-quantitative global approximation for the Stokes initial-boundary value problem Higaki, Mitsuo Analysis of PDEs We establish the first quantitative Runge approximation theorem, with explicit $L^2$-estimates, for the 3d nonstationary Stokes system on a bounded spatial domain. This result addresses the two primary limitations of the qualitative result [H.-Sueur, 2025] obtained in collaboration with Franck Sueur: first, it bypasses the non-constructive Hahn-Banach theorem used in [H.-Sueur, 2025], precluding quantitative estimates; and second, it extends the scope of the theory from interior approximations to the physically important initial-boundary value problem. Our proof is founded on the modern quantitative framework of [Rüland-Salo, 2019], which we adapt to the Stokes system by combining semigroup theory with a quantitative approximation for the associated resolvent problem. |
| title | An $L^2$-quantitative global approximation for the Stokes initial-boundary value problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.16079 |