Motion simplified equations for an incompressible fluid method of asymptotic expansion

Formulated boundary problem of flow around the concave surface of a viscous incompressible fl uid, the solution of which is accepted method of matched asymptotic expansions. The method of matched asymptotic expansions characterized by the loss of boundary conditions. One can not expect that the outer expansion will satisfy the conditions imposed are in the inner region, and conversely, the inner expansion generally will not satisfy the conditions in a remote area. But the loss is compensated splicing conditions. Splicing is the main feature of the method. The possibility of matching based on the existence of the overlap region, which are suitable both internal and external expansion. Using this overlap, you can get the exact relationship between the finite partial sums. The implementation of this option is only feasible for the perturbation parameter, which is inhomogeneous in the coordinates, and the coordinates for the disturbance, which is inhomogeneous in other coordinates. You can not splice two different parametric decomposition, such as the expansion for large and small values of the Reynolds number and Mach number; it is impossible to splice two different coordinate expansions, such as the expansion of small and large values of time or distance. Such rows can overlap in the sense that they have a common domain of convergence, but the process of analytic continuation gives only approximate relation to a finite number of members. The existence of a region of overlap means that the internal expansion external expansion should be up to the relevant procedure in line with the outer expansion of internal expansion. This principle applies to higher-order approximation, while maintaining further terms in the asymptotic expansion. We can assume that the number of members may be different for internal and external expansions as the normal order of splicing requires margin per unit for even steps.