Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows

Oleksiy V. Kapustyan; Pavlo O.  Kasyanov; José Valero; Michael Z. Zgurovsky

doi:10.3934/dcdsb.2018146

Article Contents

2018, Volume 23, Issue 3: 1155-1176. Doi: 10.3934/dcdsb.2018146

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Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows

1.
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
2.
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine
3.
Universidad Miguel Hernandez de Elche, Centro de Investigación Operativa, Avda. Universidad s/n, 03202-Elche (Alicante), Spain

* Corresponding author
* Corresponding author

Received: February 28, 2017

Revised: May 31, 2017

Early access: February 2018

Published: June 2018

The first two authors were partially supported by the State Fund for Fundamental Research of Ukraine under grant GP/F66/14921 and by the Grant of the National Academy of Sciences of Ukraine 2290/2018. The third author was partially supported by Spanish Ministry of Economy and Competitiveness and FEDER, projects MTM2015-63723-P and MTM2016-74921-P, and by Junta de Andalucía (Spain), project P12-FQM-1492.

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Abstract

In this paper we prove the existence of global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of complex fluids. We also show that the attractors tend to the set of all complete bounded trajectories of the original problem when the parameter of the approximations goes to zero.

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Mathematics Subject Classification: 35B40, 35B41, 35K55, 37B25.

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