Abstract
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.
Highlights
This paper is devoted to the perturbed Navier-Stokes equations in a cylindrical coordinate system assuming rotationally symmetric flow ρ ∂ vx ∂t + ρ vx ∂ vx ∂x ρ vr ∂ vx ∂r ρ vx ∂ vr ∂r r vr =μ ∂ vx ∂ x r ∂ ∂r r ∂vx + ∂vr ∂r ∂x
1 Introduction This paper is devoted to the perturbed Navier-Stokes equations in a cylindrical coordinate system assuming rotationally symmetric flow ρ
The aim of this paper is to extend the existence result of [ ] concerning the twodimensional fluid-structure interaction problem to the radially symmetric case expressed in terms of the cylindrical coordinate system
Summary
< ε , < δ α, κ and given a function h ∈ C ([–L–, L+] × [ , T]) satisfying Be satisfied, and let L(η) = (u, q, z) be the corresponding solution of problem ). Let (u , q , z ) and (u , q , z ) be weak solutions of the initial boundary value problem
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