  This paper deals with the fully parabolic chemotaxis-convection model with
sensitivity functions for tumor angiogenesis, \begin{align*}
  \begin{cases}
  u_t=\Delta u-\nabla \cdot (u\chi_1(v)\nabla v)
  +\nabla \cdot (u\chi_2(w)\nabla w),
  &x \in \Omega,\ t>0,
  \\[1.05mm]
  v_t=\Delta v+\nabla \cdot (v\xi(w)\nabla w)+\alpha u-\beta v,
  &x \in \Omega,\ t>0,
  \\[1.05mm]
  w_t=\Delta w+\gamma u-\delta w,
  &x \in \Omega,\ t>0
  \end{cases}
  \end{align*} under homogeneous Neumann boundary conditions and initial
conditions, where $\Omega \subset \mathbb{R}^n$ $(n \le 3)$ is a bounded domain
with smooth boundary, $\chi_1, \chi_2, \xi$ are functions satisfying some
conditions and $\alpha, \beta, \gamma, \delta>0$ are constants. The purpose of
this paper is to establish global existence and boundedness in this system.
