Hyperbolic quasilinear covariant first-order equations of divergent type for vector fields on $\mathbb{R}^3$

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 $t\in\mathbb{R}$ of vector fields $\boldsymbol{v}(\boldsymbol{x},t)$, $\boldsymbol{x}\in\mathbb{R}^3$, which are invariant under translations in time $t\in\mathbb{R}$ and space $\mathbb{R}^3$ and transform covariantly under transformations from the group $\mathbb{O}_3$ of rotations of the space $\mathbb{R}^3$. This class is compared with the class of similar equations, which are hyperbolic in the sense of Friedrichs.