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Uniqueness of Plane Stationary Navier–Stokes Flow Past an Obstacle
Archive for Rational Mechanics and Analysis ( IF 2.6 ) Pub Date : 2021-03-23 , DOI: 10.1007/s00205-021-01640-9 Mikhail Korobkov , Xiao Ren
中文翻译:
平面平稳Navier–Stokes流越过障碍的唯一性
更新日期:2021-03-23
Archive for Rational Mechanics and Analysis ( IF 2.6 ) Pub Date : 2021-03-23 , DOI: 10.1007/s00205-021-01640-9 Mikhail Korobkov , Xiao Ren
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:
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)。