Weighted analogue of LBB conditions for solving the Stokes problem with model boundary conditions in a domain with singularity

Alexey V. Rukavishnikov

Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russian Federation

Abstract: The concept of a $R_{\nu}$-generalized solution for the Stokes problem with model boundary conditions in a domain with a corner singularity is defined in the paper. Weighted analogue of the Ladyzhenskaya–Babuska–Brezzi conditions in a domain with a re-entrant corner is proven.

Keywords: corner singularity, Stokes problem with model boundary conditions, $R_{\nu}$-generalized solution.

UDC: 517.95

Received: 10.08.2024
Received in revised form: 15.09.2024
Accepted: 24.10.2024

Language: English