Analytical Solution of Second Stokes Problem on Behavior of Gas over Oscillation Surface. Part II: Mathematical Apparatus for Solving of Problem

TL;DR

This paper develops a mathematical framework using Riemann boundary value problems to analytically solve the second Stokes problem, describing the behavior of a rarefied gas over an oscillating surface.

Contribution

It introduces a new analytical method involving factorization and integral representations to solve the second Stokes problem for rarefied gases.

Findings

Derived integral representations for the factorizing function

Established a factorization formula for the dispersion function

Identified zeros of the dispersion function using the factorization

Abstract

In the present work the mathematical apparatus necessary for solving of second Stokes problem is developed. Second Stokes problem is the problem about behavior of rarefied gas filling half-space. A plane, limiting half-space, makes harmonious oscillations in this plane. At the heart of the analytical decision the homogeneous Riemann boundary value problem lays. The decision of homogeneous Riemann problem is function, factorizing problem. Integral representations for factorizing function is deduced. With the help of factorizing function the factorization formula for dispersion function is proved. Zero of dispersion function are searched by means of the factorization formula of dispersion function.