  Given an initial $C^1$ hypersurface and a time-dependent vector field in a
Sobolev space, we prove a time-global existence of a family of hypersurfaces
which start from the given hypersurface and which move by the velocity equal to
the mean curvature plus the given vector field. We show that the hypersurfaces
are $C^1$ for a short time and, even after some singularities occur, almost
everywhere $C^1$ away from higher multiplicity region.
