  In this paper we are concerned with the local well-posedness of the unsteady
potential flows near a space corner of right angle, which could be formulated
as an initial-boundary value problem of a hyperbolic equation of second order
in a cornered-space domain. The corner singularity is the key difficulty in
establishing the local well-posedness of the problem. Moreover, the boundary
conditions on both edges of the corner angle are of Neumann-type and fail to
satisfy the linear stability condition, which makes it more difficult to
establish a priori estimates on the boundary terms in the analysis. In this
paper, extension methods will be updated to deal with the corner singularity,
and, based on a key observation that the boundary operators are co-normal, new
techniques will be developed to control the boundary terms.
