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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. [ABSTRACT FROM AUTHOR]

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. The case of the boundary value with a nonzero flow rate is considered. 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 is constructed. The justification of the asymptotic expansion and the existence of a solution are proved in the second part of the paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The initial boundary value problem for the non-steady Stokes system is considered in bounded domains with the boundary having a peak-type singularity (power cusp singularity). The case of the boundary value with a nonzero time-dependent flow rate is studied. The formal asymptotic expansion of the solution near the singular point is constructed. This expansion contains both the outer asymptotic expansion and the boundary-layer-in-time corrector with the 'fast time' variable depending on the distance to the cusp point. The solution of the problem is constructed as the sum of the asymptotic expansion and the term with finite energy. [ABSTRACT FROM AUTHOR]