We study the exterior problem for stationary Navier–Stokes equations in two dimensions describing a viscous incompressible fluid flowing past an obstacle. It is shown that, at small Reynolds numbers, the classical solutions constructed by Finn and Smith are unique in the class of D-solutions (that is, solutions with finite Dirichlet integral). No additional symmetry or decay assumptions are required. This result answers a long-standing open problem. In the proofs, we developed the ideas of the classical Ch. Amick paper (Acta Math. 1988).

中文翻译：

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平面平稳Navier–Stokes流越过障碍的唯一性

我们研究二维固定维氏Navier-Stokes方程的外部问题，该方程描述了流过障碍物的粘性不可压缩流体。结果表明，在较小的雷诺数下，由Finn和Smith构造的经典解在D-解（即具有有限Dirichlet积分的解）的类中是唯一的。无需其他对称性或衰减假设。这个结果回答了一个长期存在的开放性问题。在证明中，我们提出了经典Ch。阿米克论文（Acta Math。1988）。