The Second Stokes Problem with Specular - Diffusive Boundary Conditions in Kinetic Theory

TL;DR

This paper introduces a novel method for solving the second Stokes problem with mixed boundary conditions in kinetic theory, enabling highly accurate solutions through integral equations and series expansions.

Contribution

A new approach representing boundary conditions as sources in the kinetic equation, leading to solutions via Fredholm integral equations and Neumann series.

Findings

Method achieves arbitrary accuracy in solutions.

Reduces boundary problems to Fredholm integral equations.

Provides explicit solutions using Neumann series.

Abstract

The second Stokes problem with specular - diffusive boundary conditions of the kinetic theory is considered. The new method of the decision of the boundary problems of the kinetic theory is applied. The method allows to receive the decision with any degree of accuracy. At the basis of a method lays the idea of representation of a boundary condition on distribution function in the form of a source in the kinetic equation. By means of integrals Fourier the kinetic equation with a source is reduced to the integral equation of Fredholm type of the second kind. The decision is received in the form of Neumann's series.