Korteweg-deVries equation, I. Global existence of smooth solutions

Here D-= -, Main theorem.In this note we state the result only.The detailed proof will be published elsewhere.We treat in this note (I) the global existence of smooth solutions of the Cauchy problem or the KdV equation.In the ollowing note (II)[6] we show the existence of computable approx- imate solutions by the method of finite difference schemes.