Global boundedness and stabilization under small initial data condition in a two-dimensional chemotaxis-convection model

Abstract

In this paper, we consider the two-dimensional chemotaxis-convection model of capillary-sprout growth during tumor angiogenesis under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, we prove that the system possesses a global bounded solution. In addition, the asymptotic behavior of the solutions is studied.