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

Global existence and weak-strong uniqueness for chemotaxis compressible Navier-Stokes equations modeling vascular network formation