幂尖域上平稳Navier-Stokes系统的奇异解

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2021-11-26 DOI:10.3846/mma.2021.13836

K. Pileckas, A. Raciene

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引用次数: 1

摘要

在二维有界区域上，考虑稳定Navier-Stokes系统的边值问题，边界在o点处具有幂尖点奇点，研究了边值流率为非零的情况。在这种情况下，在0中有一个源/汇解必然有一个无限的狄利克雷积分。构造了奇异点附近解的形式渐近展开式，并证明了具有这种渐近分解的解的存在性。

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On singular solutions of the stationary Navier-Stokes System in Power Cusp Domains

The boundary value problem for the steady Navier–Stokes system is considered in a 2D bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with a nonzero flow rate is studied. In this case there is a source/sink in O and the solution necessarily has an infinite Dirichlet integral. The formal asymptotic expansion of the solution near the singular point is constructed and the existence of a solution having this asymptotic decomposition is proved.

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