Singular nonlinear problems for self-similar solutions of boundary-layer equations with zero pressure gradient: analysis and numerical solution

For a mathematically correct formulation and analysis of the problems referred to in the title, a new approach, different from that previously used by specialists in fluid and gas mechanics, has been developed and justified. The main initial-boundary value problem for a third-order nonlinear ordinary differential equation on the entire real axis approximately describes self-similar flow regimes of a viscous incompressible fluid in a mixing layer (a special case is the problem for a flat semi-jet). An associated singular nonlinear boundary value problem on a non-positive real semiaxis is of independent mathematical interest, and its particular solutions admit a well-known physical interpretation (problems for submerged jet, wall jet, etc.). For a substantiated mathematical formulation of these problems and their detailed analysis and numerical solution, the results on singular nonlinear Cauchy problems, smooth stable initial manifolds of solutions, and parametric exponential Lyapunov series, as well as methods of asymptotic analysis, are used. The results of numerical experiments are presented, and their physical interpretation is discussed.