PHYSICAL AND MATHEMATICAL SCIENCES

About asymptotic representation of one task of flow fluid dynamics solution

E. V. Astakhova

Voronezh State University

Abstract: The initial boundary-value problem of hydrodynamics in a plane with a barrier, considered in the article, continues a series of studies aimed at studying the asymptotic properties of solutions of nonclassical problems of mathematical physics, such as in [1]–[6]. The urgency of the work lies in the study of the smoothness of solutions in the presence of discontinuities in the boundary conditions. The main goal is to study the behavior of the solution of the problem, as well as its first derivatives in the neighborhood of the boundary. The study is based on the method of transition to the generalized problem and the theory of MacDonald-Bessel functions. Under certain conditions, the singular terms of the solution components and their derivatives are singled out.

Keywords: dynamics of viscous fluid; asymptotics; barrier; generalized solution; singularity; MacDonald-Bessel functions.

UDC: 517.95