  We show the local wellposedness of biharmonic wave maps with initial data of
sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of
the gradient of the solutions. In contrast to the wave maps equation we use a
vanishing viscosity argument and an appropriate parabolic regularization in
order to obtain the existence result. The geometric nature of the equation is
exploited to prove convergence of approximate solutions, uniqueness of the
limit, and continuous dependence on initial data.
