Bifurcation from a blood flow with variable body force

TL;DR

This paper analyzes bifurcation phenomena in blood flow with variable body forces, demonstrating the existence of small-amplitude periodic solutions using bifurcation theory, especially in cases with harmonic vorticity and external forces.

Contribution

It extends bifurcation analysis to blood flow models with variable body forces and harmonic vorticity, overcoming challenges in reducing PDEs with free boundaries to ODE systems.

Findings

Existence of a local $C^1$-curve of small-amplitude periodic solutions.

Application of Crandall-Rabinowitz bifurcation theorem to blood flow models.

Demonstration of bifurcation in blood flow with harmonic vorticity and external forces.

Abstract

This paper investigates the existence of periodic solutions in blood flow propagating through vessels with free boundary conditions via the bifurcation theory. It is rigorously proved that a local $C^1$-curve of small-amplitude periodic solutions is bifurcated. In contrast to previous studies on periodic flows that primarily focus on constant vorticity, our work emphasizes the bifurcation analysis of periodic solutions in blood flow with harmonic vorticity and external body forces. To utilize Crandall-Rabinowitz bifurcation theorem, the fundamental challenge lies in reducing a multiple variable-PDE subject to free boundary conditions to a system of one variable-ODE with fixed boundary conditions.