Plane universal streamline patterns of incompressible viscous fluids (Q1110404)

The paper is a thoroughgoing study about the old problem put by \textit{G. Hamel} [Deutsche Math. Ver. 25, 34-60 (1916)], concerning the existence of a viscous fluid movement whose streamlines and streamsurfaces are identical with those of an ideal fluid mouvement. Such flows are generally called universal and the author generalizes this notion with the condition \(\lim_{\nu \to 0}v(x,y,\nu)=v^*(x,y)\not\equiv 0\). Limiting his study to plane mouvements, he proves the main theorem of the paper: if a viscous mouvement in a plane domain is subjected to arbitrary perturbations of the viscosity and if the flow remains unchanged or is replaced by another one with the same streamline pattern, then, the flow is universal and the streamlines are expressible in the form \(\beta_ 0x^ 2/2+\theta (x,y)=const.\); \(\beta_ 0\) is a real constant and \(\theta\) a harmonic function.