Abstract. The uniqueness and existence of generalized solutions of 'spiral curves' for the mean curvature flow with driving force is studied by an adapted level set formulation. It is shown that the curves which are given by the level set formulation are unique with respect to initial spiral curves. For given spiral curves the method of a construction of an initial datum of a level set equation is also obtained by constructing a branch of the arguments from the centers of spiral curves, which has discontinuity at the given spiral curves. IntroductionVarious motions of spiral curves are observed on the growing surface of a crystal. This phenomena is come from spiral growth that occurs with aid of a screw dislocation intersecting the surface. In 1949, F. C. Frank pointed out important role of a screw dislocation to growth of a crystal in [5]. The theory of a growth of a crystal with aid of a screw dislocation is proposed by [1]. Recently this is called spiral growth of a crystal. According to the theory in [1], the spiral curves are described by steps on the surface of a crystal, and they move by the evolution law of the formwhere V is the normal velocity, κ is the curvature of the curve, and C is a constant Figure 1. A crystal surface.which denotes the driving force. This is an interface model of spiral crystal growth. We have two types of mathematical models of this phenomena, phase-field models or interface models. A. Karma and M. Plapp ([12]) proposed a phase-field model 2000 Mathematics Subject Classification. 53C44, 35K65.