  A model of vascular network formation is analyzed in a bounded domain,
consisting of the compressible Navier-Stokes equations for the density of the
endothelial cells and their velocity, coupled to a reaction-diffusion equation
for the concentration of the chemoattractant, which triggers the migration of
the endothelial cells and the blood vessel formation. The coupling of the
equations is realized by the chemotaxis force in the momentum balance equation.
The global existence of finite energy weak solutions is shown for adiabatic
pressure coefficients $\gamma>8/5$. The solutions satisfy a relative energy
inequality, which allows for the proof of the weak--strong uniqueness property.
