Unique solvability of the cauchy problem for the equations of discrete multidimensional chiral fields,taking values on the unit sphere

One considers a discrete model of the classical field theory, defined by the action with the constraints. Here the _i s are basis vectors in the dimensional integral lattice and the functions take values in. One proves that the Cauchy problem for the equations of the motion of this model has at least one C -solution for arbitrary initial data which are consistent with the constraints. The uniqueness of the solution is established under the condition of the uniform boundedness of. In the case =2, 3, 4, the uniqueness theorem is proved without this restriction.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 217–224, 1980.In conclusion, the author wishes to express his deep gratitude to his scientific advisor, O. A. Ladyzhenskaya, for suggesting the problem and for her assistance.