Global well-posedness and decay estimates for the one-dimensional models of blood flow with a general parabolic velocity profile.

In this paper, we study the one-dimensional models of blood flow arising from the hemodynamics of aorta, which are derived from the averaging of the Navier–Stokes equations. We establish the global well-posedness and long-time behavior of the viscid 1D models of blood flow in the Sobolev space framework, where a general parabolic velocity profile is considered. Precisely speaking, we prove the global existence of smooth solution when the initial data is sufficiently small. Moreover, by combining the time-weighted energy estimates with the Green function method, we obtain the optimal time decay rate in L p (2 ≤ p ≤ ∞) norm. In addition, one can see the area-averaged axial velocity decays faster than the cross-sectional area of vessel from the Green function of the linearized system. This observation is essential to study the decay rates of our nonlinear system. [ABSTRACT FROM AUTHOR]