Abstract
Abstract 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.
Highlights
The point source/sink approach is widely used in physics and astronomy
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 justi cation of the asymptotic expansion and the existence of a solution are proved in the second part of the paper
Summary
The point source/sink approach is widely used in physics and astronomy. For example, stars are routinely treated as point sources. In the rst part of the paper the formal asymptotic expansion of the solution near the singular point is constructed. In recent papers [22, 23] the authors have studied existence of singular solutions to the stationary, timeperiodic and initial boundary value problems for the linear Stokes equations in domains having a power-cusp (peak type) singular point on the boundary.
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