Open AccessON SINGULAR SOLUTIONS OF THE STATIONARY NAVIER-STOKES SYSTEM IN POWER CUSP DOMAINS
Author(s) -
Konstantin Pileckas,
Alicija Račienė
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.13836
Subject(s) - mathematics , cusp (singularity) , singularity , mathematical analysis , bounded function , boundary value problem , asymptotic expansion , singular solution , dirichlet boundary condition , domain (mathematical analysis) , boundary (topology) , singular point of a curve , dirichlet distribution , geometry
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.