Navier--Stokes Equations with Navier Boundary Conditions for a Bounded Domain in the Plane
Navier--Stokes Equations with Navier Boundary Conditions for a Bounded Domain in the Plane
We consider solutions to the Navier--Stokes equations with Navier boundary conditions in a bounded domain $\Omega$ in ${\ensuremath{\BB{R}}}^2$ with a $C^2$-boundary $\Gamma$. Navier boundary conditions can be expressed in the form $\omega(v) = (2 \kappa - {\ensuremath{\alpha}}) v \cdot {\mbox{\boldmath $\tau$}}$ and $v \cdot \mathbf{n} = 0$ on $\Gamma$, where …