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Uspekhi Mat. Nauk, 2014, Volume 69, Issue 2(416), Pages 149–176 (Mi umn9573)  

Dynamical systems approach to models in fluid mechanics

E. Feireisl

Mathematical Institute, Academy of Sciences of the Czech Republic

Abstract: This paper gives a survey of some recent results on the asymptotic behaviour for large time of solutions of models of complete fluid systems, meaning models including compressibility, viscosity, and/or heat conductivity of the fluids. Several concepts of solutions are introduced, and the existence of global-in-time trajectories is discussed along with general questions concerning well-posedness. Dissipativity properties are considered, and in particular, the existence of absorbing sets and the asymptotic compactness of trajectories. Finally, the existence of attractors, convergence to equilibria, and other qualitative aspects of the long-time behaviour are studied.
Bibliography: 57 titles.

Keywords: Navier–Stokes–Fourier system, weak solution, long-time behaviour.

Funding Agency Grant Number
European Research Council ERC 320078
The research leading to these results was funded by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ ERC Grant Agreement 320078.


DOI: https://doi.org/10.4213/rm9573

Full text: PDF file (700 kB)
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English version:
Russian Mathematical Surveys, 2014, 69:2, 331–357

Bibliographic databases:

UDC: 517.93
MSC: 35Q30, 76N10
Received: 27.10.2013

Citation: E. Feireisl, “Dynamical systems approach to models in fluid mechanics”, Uspekhi Mat. Nauk, 69:2(416) (2014), 149–176; Russian Math. Surveys, 69:2 (2014), 331–357

Citation in format AMSBIB
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