Equivalence transformations of the Clebsch equations

E. V. Mamontov

doi:10.1007/s11202-008-0012-1

Equivalence transformations of the Clebsch equations

E. V. Mamontov

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	123-129
Number of pages	7
Journal	Siberian Mathematical Journal
Volume	49
Issue number	1
DOIs	https://doi.org/10.1007/s11202-008-0012-1
State	Published - Jan 2008
Externally published	Yes

Funding

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).

Funders	Funder number
State Maintenance Program for the Leading Scientific Schools of the Russian Federation	NSh–5245.2006.1
Russian Foundation for Basic Research	05–01–00080
Siberian Branch, Russian Academy of Sciences	2.15

Keywords

Arbitrary element
Clebsch equations
Equivalence transformation
Ideal incompressible fluid

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10.1007/s11202-008-0012-1

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AB - 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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Equivalence transformations of the Clebsch equations

Abstract

Funding

Keywords

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