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A computer‐assisted instability proof for the Orr‐Sommerfeld problem with Poiseuille flow
Author(s) -
Watanabe Y.,
Plum M.,
Nakao M.T.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700158
Subject(s) - hagen–poiseuille equation , eigenvalues and eigenvectors , computer assisted proof , instability , flow (mathematics) , stability (learning theory) , mathematics , computer science , calculus (dental) , mechanics , physics , algorithm , medicine , automated theorem proving , dentistry , quantum mechanics , machine learning
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.