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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.

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.

### MSC:

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 |