ON SINGULAR SOLUTIONS OF THE STATIONARY NAVIER-STOKES SYSTEM IN POWER CUSP DOMAINS | Zendy

Konstantinas Pileckas | Zendy; Alicija Račienė | Zendy

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ON SINGULAR SOLUTIONS OF THE STATIONARY NAVIER-STOKES SYSTEM IN POWER CUSP DOMAINS

Author(s) -

Konstantinas Pileckas,

Alicija Račienė

Publication year - 2021

Publication title -

mathematical modelling 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.

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