Non-stationary Navier-Stokes equations in 2D power-cusp domain

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.
To find a solution, we first construct the formal asymptotic expansion $(U^J, P^J)$ of it near the singular point, and then we find a solution in the form $u = \zeta U^J + v$, where $\zeta$ is cutoff function and $v$ has finite dissipation of energy.