We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-21, author = {Ji\v r\'\i\ Neustupa and Patrick Penel}, title = {The Navier-Stokes equation with inhomogeneous boundary conditions based on vorticity}, journal = {Banach Center Publications}, volume = {83}, year = {2008}, pages = {321-335}, zbl = {1154.35069}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-21} }
Jiří Neustupa; Patrick Penel. The Navier-Stokes equation with inhomogeneous boundary conditions based on vorticity. Banach Center Publications, Tome 83 (2008) pp. 321-335. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-21/