A boundary integral approach to analyze the viscous scattering of a pressure wave by a rigid body.

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potentials and also a stress tensor. Correspondingly, a viscous double-layer potential is defined. The properties of all these potentials are investigated.By representing the scattered field as a combination of a single-layer viscous potential and a double-layer viscous potential the problem is reduced to the solution of a singular vectorial integral equation of Fredholm type of the second kind.In the case where the stress vector on the boundary is the main quantity of interest the corresponding boundary singular integral equation is proved to have a unique solution.