Generalized Navier–Stokes equations with non-standard conditions for blood flow in atherosclerotic artery

Applicable Analysis, Vol. 95, Issue 8 (2016), http://dx.doi.org/10.1080/0003
http://www.tandfonline.com/doi/abs/10.1080/00036811.2015.1068297?journalCode=gapa20

In this paper, we consider the blood flow in a stenosed artery. We give an analytical study of the equations for a non-Newtonian fluid modeling the blood for which the behavior is obeying to Carreau’s law. The case we treat is different than classic cases where the total pressure is in the natural boundary conditions. For this, we use the Faedo–Galerkin method to prove the existence of a weak solution for the fluid problem. Then we use a coupled approach between the fluid equations and the solid model of the arterial wall and the atheromatous plaque. A special attention is paid to the effects of the wall motion on the local fluid displacement, on the stresses, and on strains in the diseased arterial wall. These relevant quantities are analyzed extensively through numerical results.