This article is cited in 3 papers

Equivalence transformations of the Clebsch equations

E. V. Mamontov

M. A. Lavrent'ev Institute of Hydrodynamics

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.

Keywords: ideal incompressible fluid, Clebsch equations, arbitrary element, equivalence transformation.

UDC: 533+517.958

Received: 25.10.2006

 English version: Siberian Mathematical Journal, 2008, 49:1, 123–129

Bibliographic databases:

• 
• 
• 
•