The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. We consider the case where the boundary value has a nonzero flux over the boundary. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point was constructed. In this, second part, the constructed asymptotic decomposition is justified, i.e., existence of the solution which is represented as the sum of the constructed asymptotic expansion and a term with finite energy norm is proved. Moreover, it is proved that the solution represented in this form is unique.

中文翻译：

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2D功率尖点域中的非平稳Navier–Stokes方程

在边界为幂尖奇点O的二维有界域中研究了非平稳Navier-Stokes方程的初始边值问题。我们考虑边界值在边界上具有非零通量的情况。在这种情况下，O中有一个源/汇，所需的解具有无限的能量积分。在本文的第一部分中，构造了奇异点附近解的形式渐近展开。在第二部分中，证明了构造的渐近分解是合理的，即证明了溶液的存在性，该解表示为构造的渐近展开的总和，并且具有有限能量范数的项。此外，证明以这种形式表示的解决方案是唯一的。