Biharmonic wave maps: local wellposedness in high regularity

We show a local wellposedness result for biharmonic wave maps with initial data of sufficiently high Sobolev regularity. Moreover, we obtain a blow-up criterion for these 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 the approximate solutions and uniqueness of the limit.