Well-posedness Of An Initial-boundary Value Problem In Blood Flow

The study of blood flow is one of the most important fields in the research of biological science. With the development of the biological science and mathematical theory in recent years, mathematical theory of blood flow has been widely appreciated and a number of interesting results have been developed.Blood flow model has many essential differences with classical fluid mechanics, and has its own complexity. For example, the vessel wall is a free boundary, the interaction between the blood flow and the vessel wall, the change of the pressure drop between the inlet and outlet has significant impact on the blood flow and so on.In this paper we use the incompressible Navier-Stokes equation to describe the blood flow and use the elastic equation to describe the motion of the vessel wall, then we use the initial boundary value problem of the above two equations to describe the blood flow problem. Our main purpose is to establish the well-posedness of the blood flow model. This study shows certain reasonable of this model in describing the blood flow.To get the well-posedness of the initial boundary value problem for the coupled equations, we first derive the dual problem, then by using a series of a priori estimate, we get the existence, uniqueness and stability of the solution to the original problem.