Hyperbolic quasilinear covariant first-order equations of divergent type for vector fields on R³

Abstract

In this paper, we present a complete description of the class of first-order hyperbolic quasilinear equations of divergent type that describe the change in time t e R of vector fields v(x,t), x e R³ that are invariant under translations in time t e R and space R³ and transform covariantly under the action of the rotation group O₃ of the space R³. This class is compared with the class of similar equations that are hyperbolic in the sense of Friedrichs