| Abstract [eng] |
The Navier–Stokes equations serve as the foundation for modeling diverse engineering and biological systems that involve fluid dynamics. Given our focus on the application of Navier–Stokes equations in medicine, particularly in the modeling of blood circulation systems and cardiac dynamics, we concentrate our interest in the development of simplified theoretical models. In order to compute the blood flow velocity in the blood vessels considered as cylinders, it becomes necessary to prescribe a flow rate (flux) condition. Within the scope of this thesis we prove the existence and the uniqueness of the solution of time-periodic Navier–Stokes equations under minimally regular flow rate. Moreover, the Navier–Stokes equations provide a framework for modeling fluid motion in domains featuring moving walls. We consider the model of Navier–Stokes fluid motion in a pipe surrounded by an elastic wall which was developed by G. Panasenko and R. Stavre. Since physical properties of the wall are constant, we derive the fourth order PDE which depends only on one space variable and time. Finally, for the computation of the blood flow velocity within the left atrial appendage (LAA) of the human heart, with the aim of identifying stagnation zones which are linked to thrombosis according to the hypothesis of medical doctors, we develop a fully coupled patient-specific FSI model, where the blood flow is described by Navier–Stokes equations with the moving heart wall (myocardium) considered as a shell. |
