An approximation of the axially symmetric flow through a pipe-like domain with a moving part of a boundary

Boundary value problems

Jan Filo¹  Volker Pluschke² 

[1] Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia;Faculty of Natural Sciences II, Institute of Mathematics, Martin Luther University Halle-Wittenberg, Halle, Germany

关键词: perturbed Navier-Stokes equations;    artificial pressure;    fluid-structure interaction;    cylindrical coordinate system;    Schauder fixed point theorem;   

DOI  :  10.1186/1687-2770-2013-241

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this work is to study the existence of solutions for approximation of an unsteady fluid-structure interaction problem. We consider a perturbed Navier-Stokes equation in the cylindrical coordinate system assuming axially symmetric flow. A priori unknown part of the boundary (that interacts with the fluid) is governed with a linear equation of fifth order. We prove the existence of at least one weak solution as long as the boundary does not touch the axis of symmetry. An explicit expression for a class of divergence-free functions is given. MSC:35Q30, 35Q35, 35D05, 74F10, 76D03.

【 授权许可】

CC BY