Reaction of the fluid flow on time-dependent boundary perturbation

Eduard Marušić-Paloka; Igor Pažanin

doi:10.3934/cpaa.2019059

Article Contents

2019, Volume 18, Issue 3: 1227-1246. Doi: 10.3934/cpaa.2019059

This issue Previous Article Blow-up and global existence of solutions to a parabolic equation associated with the fraction p-Laplacian Next Article Symmetry of solutions to a class of Monge-Ampère equations

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: May 2019

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Abstract

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.

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Mathematics Subject Classification: 76D07, 35B25, 35B40, 76M45.

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