| Abstract: |
| In this talk, we focus on an inhomogeneous incompressible Navier-Stokes system with chemotaxis modeling vascular network in a bounded domain. Precisely, the system consists of an inhomogeneous incompressible 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 global solvability and vanishing viscosity limit of finite energy weak solutions will be investigated under suitable initial-boundary value conditions. The solutions also satisfy a relative energy inequality, which ensures the weak-strong uniqueness property. This is a joint work with Dr Yazhi Xiao and Dr Lu Yang. |
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