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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.14737 |
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| _version_ | 1866908456969043968 |
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| author | Winfield, Christopher J. |
| author_facet | Winfield, Christopher J. |
| contents | We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic degree and high oscillation frequency. Our methods involve a reformulation of the system in terms of an integro-differential equation for which certain Hilbert-space methods apply. By way of a more complete asymptotic study, we extend our results to certain fundamental solution sets, characterized according to certain multi-point boundary-value problems: Such asymptotics further enable us to produce sharp estimates as confirmation of our general results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Cowling Approximation: A Verification of Ansatz via Methods of Functional and Asymptotic Analysis Winfield, Christopher J. Mathematical Physics Solar and Stellar Astrophysics 35Q85 (Primary) 34E10, 47B93 (Secondary) We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic degree and high oscillation frequency. Our methods involve a reformulation of the system in terms of an integro-differential equation for which certain Hilbert-space methods apply. By way of a more complete asymptotic study, we extend our results to certain fundamental solution sets, characterized according to certain multi-point boundary-value problems: Such asymptotics further enable us to produce sharp estimates as confirmation of our general results. |
| title | On the Cowling Approximation: A Verification of Ansatz via Methods of Functional and Asymptotic Analysis |
| topic | Mathematical Physics Solar and Stellar Astrophysics 35Q85 (Primary) 34E10, 47B93 (Secondary) |
| url | https://arxiv.org/abs/2507.14737 |