Affiliation:
1. Department of Mathematics , Faculty of Sciences , Carthage University , Bizerte , Tunisia
Abstract
Abstract
In this paper, we provide a rigorous derivation of an asymptotic formula for the perturbation of eigenvalues associated to the Stokes eigenvalue problem with Dirichlet conditions and in the presence of small deformable inclusions. Taking advantage of the small sizes of the inclusions immersed in an incompressible Newtonian fluid having kinematic viscosity different from the background one, we show that our asymptotic formula can be expressed in terms of the eigenvalue in the absence of the inclusions and in terms of the viscous moment tensor (VMT).
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics