Инд. авторы:	Frewer M., Oberlack M., Grebenev V.N.
Заглавие:	The Dual Stream Function Representation of an Ideal Steady Fluid Flow and its Local Geometric Structure
Библ. ссылка:	Frewer M., Oberlack M., Grebenev V.N. The Dual Stream Function Representation of an Ideal Steady Fluid Flow and its Local Geometric Structure // Mathematical Physics, Analysis and Geometry. - 2014. - Vol.17. - Iss. 1-2. - P.3-25. - ISSN 1385-0172. - EISSN 1572-9656.
Внешние системы:	DOI: 10.1007/s11040-014-9138-5; РИНЦ: 23973517; РИНЦ: 21869775; SCOPUS: 2-s2.0-84905221863; WoS: 000339892900001;
Реферат:	eng: Using the methodology of Lie groups and Lie algebras we determine new symmetry and equivalence classes of the stationary three-dimensional Euler equations by introducing potential functions that are based on the so-called dual stream function representation of the steady state velocity field u(x, y, z) = a double dagger lambda(x, y, z) x a double dagger mu(x, y, z), which itself can only be defined locally. In particular an infinite dimensional Lie algebra for Beltrami fields is gained. We show that this Lie algebra generates canonical transformations of a Hamiltonian flow for the dual pair of variables and . It enables us to make the classification of a two-dimensional Riemannian manifold wherein presents the local coordinates of . Furthermore the local geometry of this manifold is explored in detail. As a result an infinite set of locally conserved currents and charges in the context of a conformal field theory is finally observed.
Ключевые слова:	Shape classification; Equivalence transformation; Beltrami fields; Dual stream function; Euler equations; Symmetries;
Издано:	2014
Физ. характеристика:	с.3-25
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