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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.

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.

In the thesis there are studied stationary, time-periodic and nonstationary Stokes problems in bounded domains having a singular point O on the boundary. We assume that there is a source or a sink of the fluid in the cusp point O. Therefore, the solutions of such problems are necessary singular. In order to represent such solutions, we construct the formal asymptotic expansion of the solution near the singular point of the boundary. By this way we reduce initially formulated problems to the case where the energy solution exists. The solution of all three problems (stationary, time-periodic and nonstationary) is found then as the sum of the asymptotic expansion and the term with finite dissipation of energy.

In the thesis there are studied stationary, time-periodic and nonstationary Stokes problems in bounded domains having a singular point O on the boundary. We assume that there is a source or a sink of the fluid in the cusp point O. Therefore, the solutions of such problems are necessary singular. In order to represent such solutions, we construct the formal asymptotic expansion of the solution near the singular point of the boundary. By this way we reduce initially formulated problems to the case where the energy solution exists. The solution of all three problems (stationary, time-periodic and nonstationary) is found then as the sum of the asymptotic expansion and the term with finite dissipation of energy.