|
|||||
|
|
Asymptotic analysis of the nonsteady viscous flow with a given flow rate in a thin pipe |
|
| Authors: | Grigory Panasenko Konstantin Pileckas |
| Institution: | 1. Laboratory of Mathematics of the University of Saint-Etienne (LAMUSE) EA 3989, University of Lyon , 23 rue P.Michelon, 42023, Saint-Etienne , France grigory.panasenko@univ-st-etienne.fr;3. Department of Mathematics and Informatics , Vilnius University , Naugarduko Str., 24, LT–03225 Vilnius , Lithuania |
| Abstract: | The nonsteady Navier–Stokes equations are considered in a thin infinite pipe with the small diameter ? in the case of the Reynolds number of order ?. The time-dependent flow rate is a given function. The complete asymptotic expansion is constructed and justified. The error estimate of order O(? J ) for the difference of the exact solution and the J-th asymptotic approximation is proved for any real J. |
| Keywords: | Navier--Stokes equations Poiseuille flow thin pipe asymptotics |