On singular solutions of the initial boundary value problem for the Stokes system in a power cusp domain

Abstract

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.

Keywords:

• Non-stationary Stokes problem
• power cusp domain
• singular solutions
• asymptotic expansion

AMS Subject Classifications:

• 35Q30
• 35A20
• 76D07
• 76D10
• 76M45
• 76D03

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of K. Pileckas was funded by the Research Council of Lithuania [grant number S-MIP-17-68].