On pseudo-plane motions (Q1270670)

The author reconsiders an old problem of the complete solvability of the Navier-Stokes equations. Namely, he investigates steady, isochoric motions called usually ``pseudo-plane motions of the first kind''. The method of the study is based on the vectorial three-dimensional calculus. The author establishes conditions for existence of such solutions. In particular, the paper contains conditions for circulation-preserving motion, and the study of the cases \(\text{rot }\omega= 0\) (\(\omega= \text{rot }\vec v\)) and \(h/v>0\), where \(h= \partial\omega_b/\partial n\).