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Equivalence transformations of the Clebsch equations

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Abstract

We consider the Clebsch equations describing the motion of an ideal incompressible fluid in the absence of mass forces. These equations contain an arbitrary element, namely a function of three variables. We find the equivalence transformations of the variables which act on the arbitrary element and preserve the structure of the equations. The equivalence transformation is pointed out that takes the arbitrary element to zero. Some examples are given.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Novosibirsk, Russia

    E. V. Mamontov

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  1. E. V. Mamontov
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Correspondence to E. V. Mamontov.

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Original Russian Text Copyright © 2008 Mamontov E. V.

The author was partially supported by the Russian Foundation for Basic Research (Grant 05-01-00080), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-5245.2006.1), and the Integration Grant of the Siberian Division of the Russian Academy of Sciences (No. 2.15). Novosibirsk.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 153–160, January–February, 2008.

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Mamontov, E.V. Equivalence transformations of the Clebsch equations. Sib Math J 49, 123–129 (2008). https://doi.org/10.1007/s11202-008-0012-1

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  • DOI: https://doi.org/10.1007/s11202-008-0012-1

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