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.

中文翻译：

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分析刚体对压力波的粘性散射的边界积分方法。

论文给出了求解刚体对压力波的粘性散射问题的边界积分方程。使用这个数学工具证明了唯一性和存在定理。由于边界条件是根据速度来写的，因此得到了求解该问题的矢量边界积分方程。该论文介绍了单层粘性势和应力张量。相应地，定义了粘性双层势。研究了所有这些势的性质。通过将散射场表示为单层粘性势和双层粘性势的组合，问题被简化为二阶 Fredholm 型奇异矢量积分方程的解种类。