المجلة الدولية للعلوم والتقنية

This paper is concerned with existence the local solution of three dimensional compressible chemotaxis system (Cauchy problem of a hyperbolic- parabolic model of vasculogenesis) with chemoattractant. We show the existence of local solutions by the energy method, and using induction, integral by parts, Cauchy–Schwarz inequality, Holder inequality, and Gronwall's inequality in proving steps of local solution existence. Keywords: Chemotaxis system, Cauchy problem of a hyperbolic–parabolic model of vasculogenesis, energy method, Cauchy–Schwarz inequality, Holder inequality and Gronwall’s inequality