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Mathematical and numerical study of nonlinear problems in fluid mechanics. (English) Zbl 0633.76025
Differential equations and their applications, Equadiff. 6, Proc. 6th Int. Conf., Brno/Czech. 1985, Lect. Notes Math. 1192, 3-16 (1986).
[For the entire collection see Zbl 0595.00009.]
The study of flow problems in their generality is very difficult since real flows are three-dimensional, nonstationary, viscous with large Reynolds numbers, rotational, turbulent, sometimes also more-fase and in regions with a complicated geometry. Therefore, we use simplified, usually two-dimensional and non-viscous models. (The effects of viscosity are taken into account additionally on the basis of the boundary layer theory.) Here we give a survey of results obtained in the study of boundary value problems describing two-dimensional, non-viscous, stationary or quasistationary incompressible or subsonic compressible flows with the use of a stream function.

76D05 Navier-Stokes equations for incompressible viscous fluids
76G25 General aerodynamics and subsonic flows
35Q30 Navier-Stokes equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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