On Singular Solutions of the Stationary Navier-Stokes System in Power Cusp Domains

被引：0

作者：

Pileckas, Konstantinas ^{[1
]}

Raciene, Alicija ^{[1
]}

机构：

[1] Vilnius Univ, Inst Appl Math, Naugarduko G 24, LT-03225 Vilnius, Lithuania

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2021年 / 26卷 / 04期

关键词：

stationary Navier-Stokes problem; power cusp domain; singular solutions; asymptotic expansion; BOUNDARY-VALUE-PROBLEMS; EQUATIONS; COMPONENTS; EXISTENCE; FLOW;

D O I：

10.3846/mma.2021.13836

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：651 / 668

页数：18

共 50 条

[31] Strong solutions of the Navier-Stokes equations with singular data
Kozono, Hideo
Shimizu, Senjo
MATHEMATICAL ANALYSIS IN FLUID MECHANICS: SELECTED RECENT RESULTS, 2018, 710 : 163 - 173
[32] Isolated Singularity for the Stationary Navier-Stokes System
Choe, Hi Jun
Kim, Hyunseok
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2000, 2 (02) : 151 - 184
[33] On the Dimension of the Singular Set of Solutions to the Navier-Stokes Equations
Robinson, James C.
Sadowski, Witold
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 309 (02) : 497 - 506
[34] On symmetric Leray solutions of the stationary Navier-Stokes equations
Russo A.
Ricerche di Matematica, 2011, 60 (1) : 151 - 176
[35] On very weak solutions of the stationary Navier-Stokes equations
Kim H.
ANNALI DELL'UNIVERSITA' DI FERRARA, 2009, 55 (2) : 279 - 287
[36] MARTINGALE AND STATIONARY SOLUTIONS FOR STOCHASTIC NAVIER-STOKES EQUATIONS
FLANDOLI, F
GATAREK, D
PROBABILITY THEORY AND RELATED FIELDS, 1995, 102 (03) : 367 - 391
[37] STRUCTURE OF SET OF STATIONARY SOLUTIONS OF NAVIER-STOKES EQUATIONS
FOIAS, C
TEMAM, R
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1977, 30 (02) : 149 - 164
[38] ON THE EXISTENCE OF STATIONARY SOLUTIONS TO COMPRESSIBLE NAVIER-STOKES EQUATIONS
VALLI, A
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1987, 4 (01): : 99 - 113
[39] An estimate of the solutions of a stationary problem for the navier-stokes equations
Solonnikov V.A.
Journal of Mathematical Sciences, 2000, 101 (5) : 3563 - 3569
[40] ON STATIONARY SOLUTIONS OF NAVIER-STOKES EQUATIONS IN 2 DIMENSIONS
FINN, R
SMITH, DR
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1967, 25 (01) : 26 - &

← 1 2 3 4 5 →