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Systems of hydrodynamic type equations derived from the Navier-Stokesequations and the boundary layer equations are considered. A transformation ofthe Crocco type reducing the equation order for the longitudinal velocitycomponent is described. The issues of nonlinear stability of the obtainedsolutions are studied. It is found that a specific feature of many solutions ofthe Navier-Stokes equations is instability. The nonlinear instability ofsolutions is proved by a new exact method, which may be useful for the analysisof other nonlinear physical models and phenomena.

Equations of hydrodynamic type: exact solutions, reduction of order, transformations, and nonlinear stability/unstability