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Abstract
In this paper we present computerassisted proofs of a number of results in theoretical fluid dynamics and in quantum mechanics. An algorithm based on interval arithmetic yields provably correct eigenvalue enclosures and exclosures for nonselfadjoint boundary eigenvalue problems, the eigenvalues of which are highly sensitive to perturbations. We apply the algorithm to: the OrrSommerfeld equation with Poiseuille profile to prove the existence of an eigenvalue in the classically unstable region for Reynolds number R=5772.221818; the OrrSommerfeld equation with Couette profile to prove upper bounds for the imaginary parts of all eigenvalues for fixed R and wave number α; the problem of natural oscillations of an incompressible inviscid fluid in the neighbourhood of an elliptical flow to obtain information about the unstable part of the spectrum off the imaginary axis; Squire's problem from hydrodynamics; and resonances of onedimensional Schrödinger operators.
Original language  English 

Pages (fromto)  6581 
Number of pages  17 
Journal  LMS Journal of Computation and Mathematics 
Volume  13 
DOIs  
Publication status  Published  2010 
Keywords
 eigenvalue
 enclosures
 exclosures
 hydrodynamics
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 1 Finished

Spectral Theory of Block Operator Matrices
EPSRC (Engineering and Physical Sciences Research Council)
1/09/07 → 30/11/09
Project: Research