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

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