Generalization of compressible fluid equations in terms of complexified octonions

Abstract

Using the attractive properties of octonion algebra, an alternative formulation has been proposed for the Maxwell-type equations of compressible fluids. Although the origins of electromagnetic theory and fluid mechanics are completely different, a series of suitable and elegant 8-dimensional equations have been derived in a form similar to electromagnetic, gravitational counterparts previously given in relevant literature. Moreover, the corresponding matrix representations of derived expressions have also been presented after describing the connections between the algebraic properties of Cayley–Dickson octonions and some pseudo-real matrices.