| Title |
Time periodic Navier-Stokes equations in a thin tube structure / |
| Authors |
Juodagalvytė, Rita ; Panasenko, Grigory ; Pileckas, Konstantinas |
| DOI |
10.1186/s13661-020-01334-3 |
| Full Text |
|
| Is Part of |
Boundary value problems.. London : Springer Open. 2020, vol. 2020, iss. 1, art. no. 28, p. 1-35.. ISSN 1687-2770 |
| Keywords [eng] |
Time periodic Navier-Stokes equations ; Thin structures ; Existence and uniqueness of a solution ; Asymptotic expansion ; Method of asymptotic partial decomposition of the domain (MAPDD) |
| Abstract [eng] |
The time periodic Navier-Stokes equations are considered in the three-dimensional and two-dimensional settings with Dirichlet boundary conditions in thin tube structures. These structures are finite union of thin cylinders (thin rectangles in the case of dimension two), where the small parameter epsilon is the ratio of the hight and the diameter of the cylinders. We consider the case of finite or big coefficient before the time derivative. This setting is motivated by hemodynamical applications. Theorems of existence and uniqueness of a solution are proved. Complete asymptotic expansion of a solution is constructed and justified by estimates of the difference of the exact solution and truncated series of the expansion in norms taking into account the first and second derivatives with respect to the space variables and the first derivative in time. The method of asymptotic partial decomposition of the domain is justified for the time periodic problem. |
| Published |
London : Springer Open |
| Type |
Journal article |
| Language |
English |
| Publication date |
2020 |
| CC license |
|
