  Using the conservation laws for charge, energy, momentum, and angular
momentum, we derive hydrodynamic equations for the charge density, local
temperature, and fluid velocity, as well as for the spin tensor, starting from
local equilibrium distribution functions for particles and antiparticles with
spin 1/2. The resulting set of differential equations extend the standard
picture of perfect-fluid hydrodynamics with a conserved entropy current in a
minimal way. This framework can be used in space-time analyzes of the evolution
of spin and polarization in various physical systems including high-energy
nuclear collisions. We demonstrate that a stationary vortex, which exhibits
vorticity-spin alignment, corresponds to a special solution of the
spin-hydrodynamical equations.
