Kida, Teruhiko An asymptotic approach on Lagerstrom mathematical model for viscous flow at low Reynolds numbers. (English) Zbl 0666.76054 Bull. Univ. Osaka Prefecture, Ser. A 36, No. 2, 83-97 (1987). An approach of using an integral equation was proposed by the author to obtain asymptotic solutions of the problems in fluid dynamics, and has been applied to the problem at low Reynolds numbers. To show the rationality, this approach is used for the mathematical model oiriginally proposed by Lagerstrom as a model for viscous flow at low Reynolds numbers. This two-point boundary value problem is transformed into an integral equation which is different from that given by D. S. Cohen, A. Fokas, P. A. Lagerstrom [SIAM J. Appl. Math. 35, 187-207 (1978; Zbl 0392.76024)], and the inner and outer solutions are obtained from the integral representation. The basic integral equation is given by taking into account the significant degenerations of the differential operator. The present representation is more useful than Cohen’s one, in a sense that the lowest approximation of the inner and outer solutions are given without solving the integral equation in this problem. These asymptotic results are verified, and the rigorous proof of the existence and uniqueness of a solution is also shown. MSC: 76D05 Navier-Stokes equations for incompressible viscous fluids 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:integral equation; asymptotic solutions; lowest approximation; outer solutions; existence; uniqueness of a solution Citations:Zbl 0392.76024 PDFBibTeX XMLCite \textit{T. Kida}, Bull. Univ. Osaka Prefecture, Ser. A 36, No. 2, 83--97 (1987; Zbl 0666.76054)