Existence and regularity result for Stokes system with special inlet/outlet condition

TL;DR

This paper analyzes a viscous incompressible fluid model with special boundary conditions simulating cardiovascular flows, proving existence, uniqueness, and regularity of solutions using a modified Galerkin method.

Contribution

It introduces and mathematically validates a new boundary condition model for fluid flows with inlets and outlets, including inertia effects.

Findings

Proved existence of solutions under the new boundary conditions

Established uniqueness of solutions

Demonstrated regularity of solutions

Abstract

Our aim is to analyse special type of boundary conditions, created to simulate flows like in cardiovascular and respiratory systems. Firstly, we will describe model of viscous, incompressible fluid in a domain consisting many inlets and outlets with open dissipative boundary conditions. The conditions are augmented by the inertia terms. We are posing additional constrains on a fluid motion by a volumetric flow rates or inlet/outlet pressure. Afterwards, we will define weak formulation of the problem and its motivation. Then, we will prove mathematical correctness of proposed conditions by properly modified Galerkin method. Also, we will prove existence of a solution and its uniqueness.