  We consider the incompressible Navier-Stokes equations in a moving domain
whose boundary is prescribed by a function $\eta=\eta(t,y)$ (with $y\in\mathbb
R^2$) of low regularity. This is motivated by problems from fluid-structure
interaction. We prove partial boundary regularity for boundary suitable weak
solutions assuming that $\eta$ is continuous in time with values in the
fractional Sobolev space $W^{2-1/p,p}_y$ for some $p>15/4$ and we have
$\partial_t\eta\in L_t^{3}(W^{1,q_0}_y)$ for some $q_0>2$.
  The existence of boundary suitable weak solutions is a consequence of a new
maximal regularity result for the Stokes equations in moving domains which is
of independent interest.
