Abstract
This paper presents a computer-assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. A numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described. Some verification results confirm the effectiveness of the method. This constitutes the first strict mathematical instability proof for the Poiseuille flow.
| Original language | English |
|---|---|
| Pages (from-to) | 5-18 |
| Number of pages | 14 |
| Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |
| Volume | 89 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2008 Jan |
| Externally published | Yes |
Keywords
- Computer-assisted proof
- Non-selfadjoint eigenvalue problem
- Orr-sommerfeld equation
- Poiseuille flow
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mechanics
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Cite this
Watanabe, Y., Plum, M., & Nakao, M. T. (2008). A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 89(1), 5-18. https://doi.org/10.1002/zamm.200700158