Asymptotic stability of homogeneous solutions of incompressible stationary Navier-Stokes equations

被引：10

作者：

Li, YanYan ^{[1
]}

Yan, Xukai ^{[2
]}

机构：

[1] Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[2] Oklahoma State Univ, Dept Math, 401 Math Sci Bldg, Stillwater, OK 74078 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 297卷

基金：

美国国家科学基金会;

关键词：

SIMILAR VISCOUS FLOWS; ISOLATED SINGULARITIES; WEAK SOLUTIONS; AXIAL CAUSES; L2; DECAY;

D O I：

10.1016/j.jde.2021.06.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was proved by Karch and Pilarczyk that Landau solutions are asymptotically stable under any L-2-perturbation. In our earlier work with L. Li, we have classified all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles. In this paper, we study the asymptotic stability of the least singular solutions among these solutions other than Landau solutions, and prove that such solutions are asymptotically stable under any L-2-perturbation. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：226 / 245

页数：20

共 25 条

[1]

Cannone M., 2004, HDB MATH FLUID DYNAM, VIII, P16

[2]

Goldshtik M. A., 1960, J. Appl. Math. Mech. (USSR, V24, P913

[3] ON L2 DECAY OF WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN RN [J].

KAJIKIYA, R ;

MIYAKAWA, T .

MATHEMATISCHE ZEITSCHRIFT, 1986, 192 (01) :135-148

[4] L2-asymptotic stability of singular solutions to the Navier-Stokes system of equations in R3 [J].

Karch, Grzegorz ;

Pilarczyk, Dominika ;

Schonbek, Maria E. .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 108 (01) :14-40

[5] Asymptotic Stability of Landau Solutions to Navier-Stokes System [J].

Karch, Grzegorz ;

Pilarczyk, Dominika .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 202 (01) :115-131

[6] STRONG LP-SOLUTIONS OF THE NAVIER-STOKES EQUATION IN RM, WITH APPLICATIONS TO WEAK SOLUTIONS [J].

KATO, T .

MATHEMATISCHE ZEITSCHRIFT, 1984, 187 (04) :471-480

[7]

Landau L.D., 1944, Dokl. Akad. Nauk SSSR, V43, P299

[8]

Lemarie-Rieusset P.G., 2002, CHAPMAN HALL CRC RES, V431

[9] On the movement of a viscous fluid to fill the space [J].

Leray, J .

ACTA MATHEMATICA, 1934, 63 (01) :193-248

[10] HOMOGENEOUS SOLUTIONS OF STATIONARY NAVIER-STOKES EQUATIONS WITH ISOLATED SINGULARITIES ON THE UNIT SPHERE. III. TWO SINGULARITIES [J].

Li, Li ;

Li, Yanyan ;

Yan, Xukai .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (12) :7163-7211

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