A geometric analysis of the Lagerstrom model problem
The paper is devoted to the study of the Langerstrom model which describes the viscous flow past a solid at low Reynolds number. Here, the authors analyze geometrically the corresponding boundary value problem by using methods from the theory of dynamical systems, in particular invariant manifolds. However, this well-developed method is not applicable at points, where the normal hyperbolicity is lost. As an essential part of the dynamics takes place near a line of nonhyperbolic equilibria, a blow-up transformation is introduced to resolve these singularities. This approach leads to a constructive proof of existence and local uniqueness of solutions and to a better understanding of the singular perturbation nature of the problem. In particular, the source of the logarithmic switchback phenomenon is identified.
scientific article; zbMATH DE number 2104513
scientific article