Global Existence for the Rescaled Klein-Gordon-Zakharov System

We present a cross-constrained variational method to discuss the global solution of the rescaled Klein-Gordon-Zakharov system in two and three space dimensions.By constructing a type of cross-constrained variational problem,accomplishing so-called cross-invariant manifolds under the solution flow of the Cauchy problem of the Klein-Gordon-Zakharov system and using skillful dilation transformation,we give a sufficient condition on the global existence of solution to the Cauchy problem for the Klein-Gordon-Zakharov system.The sufficient condition implies that for some large Cauchy data,the solution of the Cauchy problem for the Klein-Gordon-Zakharov system may exist globally.Furthermore,we obtain two small data criteria which answer the question: how small are the initial data,the solution to the Cauchy problem of the Klein-Gordon-Zakharov system exists globally?