# American Institute of Mathematical Sciences

May  2019, 18(3): 1227-1246. doi: 10.3934/cpaa.2019059

## Reaction of the fluid flow on time-dependent boundary perturbation

 Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Received  March 2018 Revised  July 2018 Published  November 2018

The aim of this paper is to investigate the effects of time-dependent boundary perturbation on the flow of a viscous fluid via asymptotic analysis. We start from a simple rectangular domain and then perturb the upper part of its boundary by the product of a small parameter $\varepsilon$ and some smooth function $h(x, t)$. The complete asymptotic expansion (in powers of $\varepsilon$) of the solution of the evolutionary Stokes system has been constructed. The convergence of the expansion has been proved providing the rigorous justification of the formally derived asymptotic model.

Citation: Eduard Marušić-Paloka, Igor Pažanin. Reaction of the fluid flow on time-dependent boundary perturbation. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1227-1246. doi: 10.3934/cpaa.2019059
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