Dynamical systems approach to models in fluid mechanics

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.