| Abstract: |
| We consider the evolutionary Stokes system subject to the
so-called dynamic boundary condition
\[
\beta \partial_t u + \alpha u + \nu[(Du)n]_\tau = h
\qquad \textrm{on } \partial \Omega
\]
where $Du$ is the symmetric velocity gradient,
$n$ is outer normal, and subscript $\tau$ denotes
the tangential projection relative to $\partial \Omega$.
\par
Our first aim is to establish the basic $L^p$ theory,
including the existence of an analytic semigroup and
optimal $W^{k,p}$ estimates for $k=1$ and $2$.
\par
These results are then applied to related nonlinear systems:
Navier-Stokes and Cahn-Hilliard Navier-Stokes equations. |
|