Long-time behaviour of a radially symmetric fluid-shell interaction system

Tamara Fastovska

doi:10.3934/dcds.2018054

Article Contents

2018, Volume 38, Issue 3: 1315-1348. Doi: 10.3934/dcds.2018054

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Long-time behaviour of a radially symmetric fluid-shell interaction system

Tamara Fastovska^1,2, ,

1.
Kharkiv Karazin National University, 4 Svobody sq., 61077 Kharkiv, Ukraine
2.
Kharkiv Automobile and Highway National University, 25 Yaroslava Mudrogo st., 61002 Kharkiv, Ukraine

* Corresponding author: Tamara Fastovska
* Corresponding author: Tamara Fastovska

Received: March 31, 2017

Revised: August 31, 2017

Published: June 2018

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Abstract

We study the long-time dynamics of a coupled system consisting of the 2D Navier-Stokes equations and full von Karman elasticity equations. We show that this problem generates an evolution semigroup $S_t$ possessing a compact finite-dimensional global attractor.

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Mathematics Subject Classification: Primary: 74F10, 35B41; Secondary: 35Q30, 74K25.

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