Abstract
AbstractA 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 $$\gamma >8/5$$
γ
>
8
/
5
. The solutions satisfy a relative energy inequality, which allows for the proof of the weak–strong uniqueness property.
Funder
Austrian Science Fund
HORIZON EUROPE European Research Council
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Aïssa, N., Alexandre, R.: Global existence of weak solutions to an angiogenesis model. J. Evol. Eqs. 16, 877–894 (2016)
2. Ambrosi, D., Gamba, A., Serini, G.: Cell directional and chemotaxis in vascular morphogenesis. Bull. Math. Biol. 66, 1851–1873 (2004)
3. Biler, P., Brandolese, L.: On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis. Studia Math. 193, 241–261 (2009)
4. Di Francesco, M., Donatelli, D.: Singular convergence of nonlinear hyperbolic chemotaxis systems to Keller–Segel type models. Discrete Cont. Dyn. Sys. B 13, 79–100 (2010)
5. Feireisl, E.: Dynamics of Viscous Compressible Fluids. Oxford University Press, Oxford (2004)