Non-stationary Navier–Stokes equations in 2D power cusp domain-Reference-Cited by-同舟云学术

Non-stationary Navier–Stokes equations in 2D power cusp domain

Published:2021-01-01 Issue:1 Volume:10 Page:982-1010
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Pileckas Konstantin¹,Raciene Alicija¹

Affiliation:

1. Institute of Applied Mathematics, Vilnius University , Naugarduko Str., 24 , Vilnius , Lithuania

Abstract

Abstract The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. The case of the boundary value with a nonzero flow rate is considered. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point is constructed. The justification of the asymptotic expansion and the existence of a solution are proved in the second part of the paper.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2020-0164/pdf

Reference35 articles.

1. V.G. Maz’ya and B.A. Plamenevskii, Estimates in Lp and Hölder classes and the Miranda-Agmon maximum principlefor sulutions of elliptic boundary value problems in domains with singular points on the boundary, Math. Nachr., 81 (1978), 25–82. Transl.: Amer. Math. Soc. Transl., 123 (1984), no. 2, 1–56.

2. A.B. Movchan and S.A. Nazarov., Asymptotics of the stressed-deformed state near a spatial peak-type inclusion, Mekh. Kompozit. Material., 5 (1985), 792–800. Transl.: Mech. Composite Materials, 21 (1985).

3. A.B. Movchan and S.A. Nazarov, The stressed-deformed state near a vertex of a three-dimensional absolutely rigid peak imbedded in an elastic body, Prikl. Mech., 25 (1989), no. 12, 10–19. Transl.: Soviet Appl. Mech., 25 (1989).

4. S.A. Nazarov and O.R. Polyakova, Asymptotic behaviour of the stress-strain state near a spatial singularity of the boundary of the beak tip type, Prikl. Mat. Mekh., 57 (1993), no. 5, 130–149. Transl.: J. Appl. Math. Mech., 57 (1993), no. 5, 887–902.

5. S.A. Nazarov, Asymptotics of the solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain, Izv. Ross. Akad. Nauk. Ser. Mat., 58 (1994), no. 1, 92–120. Transl.: Math. Izvestiya, 44 (1995), no. 1, 91–118.

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