The Navier–Stokes equation with inhomogeneous boundary conditions based on vorticity
Volume 81 / 2008
Banach Center Publications 81 (2008), 321-335
MSC: Primary 35Q30; Secondary 76D05.
DOI: 10.4064/bc81-0-21
Abstract
We formulate a boundary value problem for the Navier–Stokes equations with prescribed ${\bf u}\cdot{\bf n}$, ${\rm curl}\, {\bf u}\cdot{\bf n}$ and alternatively $(\partial{\bf u}/\partial{\bf n})\cdot{\bf n}$ or ${\rm curl}^2\,{\bf u}\cdot{\bf n}$ on the boundary. We deal with the question of existence of a steady weak solution.
