Flows in a tube structure: Equation on the graph

Grigory Panasenko (1) , Konstantin Pileckas (2)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics and Informatics [Vilnius]

The steady-state Navier-Stokes equations in thin structures lead to some elliptic second order equation for the macroscopic pressure on a graph. At the nodes of the graph the pressure satisfies Kirchoff-type junction conditions. In the non-steady case the problem for the macroscopic pressure on the graph becomes nonlocal in time. In the paper we study the existence and uniqueness of a solution to such one-dimensional model on the graph for a pipe-wise network. We also prove the exponential decay of the solution with respect to the time variable in the case when the data decay exponentially with respect to time.

Domaines: Sciences de l'ingénieur [physics]

Grigory Panasenko, Konstantin Pileckas. Flows in a tube structure: Equation on the graph. Journal of Mathematical Physics, 2014, 55 (8), pp.081505. ⟨10.1063/1.4891249⟩. ⟨hal-02157638⟩