Global stability of large solutions for the Navier-Stokes equations with Navier boundary conditions

被引：4

作者：

Benvenutti, Maicon J. ^{[1
]}

Ferreira, Lucas C. F. ^{[2
]}

机构：

[1] Univ Fed Santa Catarina, Campus Blumenau, BR-89065300 Blumenau, SC, Brazil

[2] Univ Estadual Campinas, IMECC Dept Matemat, BR-13083859 Campinas, SP, Brazil

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 43卷

基金：

巴西圣保罗研究基金会;

关键词：

Navier-Stokes equations; Slip boundary condition; Stability; Global strong solutions; Helical solutions; ASYMPTOTIC STABILITY; L-2; STABILITY;

D O I：

10.1016/j.nonrwa.2018.03.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove global stability of strong large solutions for the 3D incompressible Navier-Stokes equations with Navier slip boundary conditions. This result is obtained under an integrable property that depends on these slip conditions. In addition, we show that strong helical solutions are global in time. Combining the latter with the stability result, we provide a class of 3D global large solutions with perturbations of helical vector-fields as initial data. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：308 / 322

页数：15

共 35 条

[1]

Antontsev S.N., 2007, RIMS KOKYUROKU BES B, V1, P21

[2] On the stability of global solutions to Navier-Stokes equations in the space [J].

Auscher, P ;

Dubois, S ;

Tchamitchian, P .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (06) :673-697

[3]

Beirao da Veiga H., 2007, Port. Math. (N.S.), V64, P377

[4]

Benvenutti MJ, 2016, DIFFER INTEGRAL EQU, V29, P977

[5] Global L2 Stability of the Nonhomogeneous Incompressible Navier-Stokes Equations [J].

Cai, Xiao Jing ;

Jiu, Quan Sen ;

Zhou, Yan Jie .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (11) :2087-2098

[6] On the global wellposedness of the 3-D Navier-Stokes equations with large initial data [J].

Chemin, Jean-Yves ;

Gallagher, Isabelle .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2006, 39 (04) :679-698

[7] On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions [J].

Clopeau, T ;

Mikelic, A ;

Robert, R .

NONLINEARITY, 1998, 11 (06) :1625-1636

[8]

da Veiga HB, 2004, ADV DIFFERENTIAL EQU, V9, P1079

[9] ON THE NONHOMOGENEOUS NAVIER-STOKES SYSTEM WITH NAVIER FRICTION BOUNDARY CONDITIONS [J].

Ferreira, Lucas C. F. ;

Planas, Gabriela ;

Villamizar-Roa, Elder J. .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (04) :2576-2595

[10] Asymptotics and stability for global solutions to the Navier-Stokes equations [J].

Gallagher, I ;

Iftimie, D ;

Planchon, F .

ANNALES DE L INSTITUT FOURIER, 2003, 53 (05) :1387-+

← 1 2 3 4 →