Abstract: In the smooth function classes,the basic equations set of atmospheric motion possesses the best stability,under this condition,its structure of solution space for local analytical solution was discussed,by which the third-class initial value problem with typicality and application was also analyzed.And in the analytic function classes,the calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind were given.In the meaning of local solution,near a appointed point,the relevant theoretical and computational problems about analytical solution of initial value problem were solved completely.Meanwhile,it is pointed out here that,with other types of problems for determining solution,the computational method and process of their stable analytical solution can be obtained in a similar way if needed.