Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl

被引：4

作者：

Kozono, Hideo ^{[1
,2
]}

Terasawa, Yutaka ^{[3
]}

Wakasugi, Yuta ^{[4
]}

机构：

[1] Waseda Univ, Fac Sci & Engn, Dept Math, Tokyo 1698555, Japan

[2] Tohoku Univ, Res Alliance Ctr Math Sci, Sendai, Miyagi 9808578, Japan

[3] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan

[4] Hiroshima Univ, Grad Sch Sci & Engn, Higashihiroshima 7398527, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 282卷 / 02期

关键词：

Axisymmetric Navier-Stokes equations; No swirl; Asymptotic behavior; Liouville-type theorems; LIOUVILLE-TYPE THEOREMS; SYMMETRIC D-SOLUTIONS; DECAY;

D O I：

10.1016/j.jfa.2021.109289

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic behavior of axisymmetric solutions with no swirl to the steady Navier-Stokes equations in the outside of the cylinder. We prove an a priori decay estimate of the vorticity under the assumption that the velocity has generalized finite Dirichlet integral. As an application, we obtain a Liouville-type theorem. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：21

共 32 条

[1] ON LERAYS PROBLEM OF STEADY NAVIER-STOKES FLOW PAST A BODY IN THE PLANE [J].

AMICK, CJ .

ACTA MATHEMATICA, 1988, 161 (1-2) :71-130

[2]

Babenko K.I., 1973, Mathematics of the USSR-Sbornik, V20, P1

[3] ALGEBRAIC L2 DECAY FOR NAVIER-STOKES FLOWS IN EXTERIOR DOMAINS [J].

BORCHERS, W ;

MIYAKAWA, T .

ACTA MATHEMATICA, 1990, 165 (3-4) :189-227

[4] Decay and Vanishing of some D-Solutions of the Navier-Stokes Equations [J].

Carrillo, Bryan ;

Pan, Xinghong ;

Zhang, Qi S. ;

Zhao, Na .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2020, 237 (03) :1383-1419

[5] Decay and vanishing of some axially symmetric D-solutions of the Navier-Stokes equations [J].

Carrillo, Bryan ;

Pan, Xinghong ;

Zhang, Qi S. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 279 (01)

[6]

Chae D, ARXIV150204793V1

[7] On Liouville type theorems for the steady Navier-Stokes equations in R3 [J].

Chae, Dongho ;

Wolf, Joerg .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (10) :5541-5560

[8] Liouville-Type Theorems for the Forced Euler Equations and the Navier-Stokes Equations [J].

Chae, Dongho .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 326 (01) :37-48

[9] Asymptotic Properties of Axis-Symmetric D-Solutions of the Navier-Stokes Equations [J].

Choe, Hi Jun ;

Jin, Bum Ja .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2009, 11 (02) :208-232

[10] ON STEADY-STATE SOLUTIONS OF THE NAVIER-STOKES PARTIAL DIFFERENTIAL EQUATIONS [J].

FINN, R .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1959, 3 (05) :381-396

← 1 2 3 4 →