A remark on the Liouville problem for stationary Navier-Stokes equations in Lorentz and Morrey spaces

被引：21

作者：

Jarrin, Oscar ^{[1
]}

机构：

[1] Univ Tecn Ambato, Direcc Invest & Desarrollo DIDE, Campus Huachi,Ave Chasquis & Rio Payamino, Ambato 180207, Ecuador

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 486卷 / 10期

关键词：

Navier-Stokes equations; Stationary system; Liouville theorem; Lorentz spaces; Morrey spaces; THEOREMS;

D O I：

10.1016/j.jmaa.2020.123871

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Liouville problem for the stationary Navier-Stokes equations on the whole space is a challenging open problem who has known several recent contributions. We prove here some Liouville type theorems for these equations provided the velocity field belongs to some Lorentz spaces and then in the more general setting of Morrey spaces. Our theorems correspond to an improvement of some recent results on this problem and contain some well-known results as a particular case. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：16

共 18 条

[1]

[Anonymous], [No title captured]

[2]

[Anonymous], 2018, ARXIV180502227

[3]

[Anonymous], [No title captured]

[4]

[Anonymous], [No title captured]

[5]

[Anonymous], 2018, THESIS

[6] Lp-Solutions of the Steady-State Navier-Stokes Equations with Rough External Forces [J].

Bjorland, Clayton ;

Brandolese, Lorenzo ;

Iftimie, Dragos ;

Schonbek, Maria E. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (02) :216-246

[7] Ill-posedness of the Navier-Stokes equations in a critical space in 3D [J].

Bourgain, Jean ;

Pavlovic, Natasa .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (09) :2233-2247

[8]

Chae D, 2016, ARXIV160407643

[9] LIOUVILLE TYPE THEOREMS FOR THE STEADY AXIALLY SYMMETRIC NAVIER-STOKES AND MAGNETOHYDRODYNAMIC EQUATIONS [J].

Chae, Dongho ;

Weng, Shangkun .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (10) :5267-5285

[10] On the Liouville theorem for the stationary Navier-Stokes equations in a critical space [J].

Chae, Dongho ;

Yoneda, Tsuyoshi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 405 (02) :706-710

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