# American Institute of Mathematical Sciences

May  2018, 23(3): 1155-1176. doi: 10.3934/dcdsb.2018146

## 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

Received  March 2017 Revised  June 2017 Published  February 2018

Fund Project: 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.

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.

Citation: Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Michael Z. Zgurovsky. Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1155-1176. doi: 10.3934/dcdsb.2018146
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