Analytic construction of the near field in a transonic flow near a thin axisymmetric body

A solution of the axisymmetric problem of unsteady transonic flow around thin bodies of revolution is proposed in the form of a double series expansion in powers of the distance to the axis of symmetry and its logarithm in a neighborhood of a given point at the symmetry axis. Chains of recurrence equations are obtained for the coefficients of the series. The convergence of the constructed series is proved by the method of special majorants. The theorem of existence and uniqueness of the solution to the boundary-value problem for a nonlinear partial differential equation with a singularity at the symmetry axis is obtained in the asymptotic model of unsteady transonic flow under consideration. Thereby the application of the proposed series is justified to the problems of unsteady transonic flow around thin axisymmetric bodies with a drift of the nonpenetration condition onto the symmetry axis. Hence, these series can be used in numerical-analytical methods and model computations.