  We study a coupled system of Navier-Stokes equation and the equation of
conservation of mass in a one-dimensional network. The system models the blood
circulation in arterial networks. A special feature of the system is that the
equations are coupled through boundary conditions at joints of the network. We
prove the existence and uniqueness of the solution to the initial-boundary
value problem, discuss the continuity of dependence of the solution and its
derivatives on initial, boundary and forcing functions and their derivatives,
develop a numerical scheme that generates discretized solutions, and prove the
convergence of the scheme.
