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This article is cited in 8 scientific papers (total in 8 papers)
Asymptotic solutions of Navier–Stokes equations and topological invariants of vector fields and Liouville foliations
V. P. Maslovab, A. I. Shafarevicha a M. V. Lomonosov Moscow State University, Moscow, Russia
b National Research University "Higher School of Economics", Moscow, Russia
Abstract:
We construct asymptotic solutions of the Navier–Stokes equations. Such solutions describe periodic systems of localized vortices and are related to topological invariants of divergence-free vector fields on two-dimensional cylinders or tori and to the Fomenko invariants of Liouville foliations. The equations describing the evolution of a vortex system are given on a graph that is a set of trajectories of the divergence-free field or a set of Liouville tori.
Keywords:
hydrodynamic equation, localized vortex, topology of Liouville foliations.
Received: 13.02.2014
Citation:
V. P. Maslov, A. I. Shafarevich, “Asymptotic solutions of Navier–Stokes equations and topological invariants of vector fields and Liouville foliations”, TMF, 180:2 (2014), 245–263; Theoret. and Math. Phys., 180:2 (2014), 967–982
Linking options:
https://www.mathnet.ru/eng/tmf8653https://doi.org/10.4213/tmf8653 https://www.mathnet.ru/eng/tmf/v180/i2/p245
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Abstract page: | 1148 | Full-text PDF : | 263 | References: | 110 | First page: | 89 |
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