Dynamical systems approach to models in fluid mechanics
Mathematical Institute, Academy of Sciences of the Czech Republic
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.
Navier–Stokes–Fourier system, weak solution, long-time behaviour.
|European Research Council
|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.
PDF file (700 kB)
Russian Mathematical Surveys, 2014, 69:2, 331–357
MSC: 35Q30, 76N10
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
\paper Dynamical systems approach to models in fluid mechanics
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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