On singular solutions of the stationary Navier-Stokes system in power cusp domains

Abstract

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.

Keywords

• stationary navier-stokes problem
• power cusp domain
• singular solutions
• asymptotic expansion