| Abstract: | The present paper presents a proof of the existence and uniqueness theorem for the solution of the axisymmetric problem with initial conditions for the Euler equations in the case of an incompressible fluid. We consider the case of the nonporous wall, and also the transpiration problem in the formulation given in 1].  Global unique solvability is proved for assumptions only on the smoothness of the conditions and for all values of the time t. The existence theorem for a small time segment in the case of a nonporous wall has been proved for the general three-dimensional problem in 2, 3]. For the proof we use a method analogous to that developed in 1] for planar flows. The a priori estimate of the vorticity which is used in the present study was obtained previously in 4],The author wishes to thank V. I. Yudovich for continued interest in the study and many valuable suggestions. |
