Irrotational vector fields, partially invariant with respect to group of rotations

• Published in: Journal of applied mathematics and mechanics Vol. 72; no. 5; pp. 530 - 535
• Main Author: Golovin, S.V.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2008; Elsevier
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Physics; Irrotational flow; Continuity equations; Invariant; Fluid mechanics; Vector fields; Rotation group; SO-3 groups
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/j.jappmathmech.2008.11.010

A geometrical description of three-dimensional irrotational vector fields which are partially invariant with respect to the
SO(3) group of rotations is given. It is shown that the motion of a continuum, that satisfies the equation of continuity and is partially invariant with respect to
SO(3), is necessarily rotational, that is, the curl of the velocity vector is non zero.