The Poiseuille type solution for the non-stationary Stokes problem in the infinite periodic pipe

Author:

Neringa~Klovien\.e

2010 Mathematics Subject Classification:

76D07, 76N10, 35Q35.

Keywords:

existence and uniqueness of solution, infinite domain, Galerkin method, non-stationary Stokes equation, periodic pipe, Poiseuille type solution, Volterra integral equation.

Abstract:

Fluids dynamic is one of the main applications of PDE in physics. In the paper, the non-stationary Stokes problem with a given flux condition is considered. The problem is analyzed in the three dimensional infinite domain (pipe) which is periodic with respect to one of the axis. The aim of the article is to prove the existence and uniqueness of the Poiseuille type solution. For solving the problem, the Galerkin approximation method is chosen, and the convergence of the constructed series and the uniqueness of the solution is proved. Under the flux condition, the unique existence of the axial pressure drop function is proved.

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klo_2015

Vol. 10 (18), 2015