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XXI International Congress of Theoretical and Applied Mechanics
Warsaw, Poland, August 15-21, 2004
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On the Nature of Virial Liapunov Functional in Hydrodynamic Instability
| V. A. Vladimirov | | Department of Mathematics, University of Hull, UK |
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There is a persistent myth of `irrationality' of `virial' Liapunov functionals used in proofs of fluid instability. The aim of the paper is to address that issue and to produce the unifying and systematic concept on introducing of `virials'. Our `virial' can be introduced via the second variation of Lagrangian, and correspondent `virial equality' is closely linked to the Jacobi equation for deviations of geodesics. This link explains the nature of `virial' as Liapunov functional. It may be considered as the `distance' between two geodesics corresponding to the main flow and perturbed flows. New applications of `virials' to instabilities both states of rest (`converse Lagrange theorems') and flows (`horseshoe instability' and `Arnold's instability') are considered and further perspectives are discussed.
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