Navier-Stokes equations with periodic boundary conditions and pressure loss

Chérif Amrouche (1) , Macaire Batchi (1, 2) , Jean Batina (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 LATEP - Laboratoire de Génie Thermique Énergétique et Procédés (EA1932)

We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure loss coefficient enables us to establish a relation on the pressure and to thus formulate an equivalent problem.

Keywords: Navier-Stokes equations; incompressible fluid; bidimensional channel; periodic boundary conditions; pressure loss

Domains: Analysis of PDEs [math.AP]

Chérif Amrouche, Macaire Batchi, Jean Batina. Navier-Stokes equations with periodic boundary conditions and pressure loss. 2007. ⟨hal-00141973⟩