Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the hausdorff dimension of their global attractors

Vincent Xiaosong Liu

doi:10.1007/bf02096584

Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the hausdorff dimension of their global attractors

Communications in Mathematical Physics ◽

10.1007/bf02096584 ◽

1992 ◽

Vol 147 (2) ◽

pp. 217-230 ◽

Cited By ~ 8

Author(s):

Vincent Xiaosong Liu

Keyword(s):

Lower Bound ◽

Hausdorff Dimension ◽

Stokes Equations ◽

Global Attractors ◽

Navier Stokes ◽

Dimensional Torus ◽

Navier Stokes Equations

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A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier-Stokes equations

Communications in Mathematical Physics ◽

10.1007/bf02108078 ◽

1993 ◽

Vol 158 (2) ◽

pp. 327-339 ◽

Cited By ~ 24

Author(s):

Vincent Xiaosong Liu

Keyword(s):

Lower Bound ◽

Hausdorff Dimension ◽

Stokes Equations ◽

Global Attractors ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Sharp Lower Bound

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Global attractors of non-autonomous Navier-Stokes equations

Interdisciplinary Mathematical Sciences - Global Attractors of Non-Autonomous Dissipative Dynamical Systems ◽

10.1142/9789812563088_0011 ◽

2004 ◽

pp. 357-383

Keyword(s):

Stokes Equations ◽

Global Attractors ◽

Navier Stokes ◽

Navier Stokes Equations

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Two models of truncated Navier–Stokes equations on a two-dimensional torus

The Physics of Fluids ◽

10.1063/1.864156 ◽

1983 ◽

Vol 26 (2) ◽

pp. 433 ◽

Cited By ~ 20

Author(s):

Valter Franceschini

Keyword(s):

Stokes Equations ◽

Navier Stokes ◽

Two Dimensional ◽

Dimensional Torus ◽

Navier Stokes Equations

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Truncations to 12, 14 and 18 modes of the Navier-Stokes equations on a two-dimensional torus

Meccanica ◽

10.1007/bf02336933 ◽

1985 ◽

Vol 20 (3) ◽

pp. 207-230 ◽

Cited By ~ 15

Author(s):

Valter Franceschini ◽

Claudio Tebaldi

Keyword(s):

Stokes Equations ◽

Navier Stokes ◽

Two Dimensional ◽

Dimensional Torus ◽

Navier Stokes Equations

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On global attractors of the 3D Navier–Stokes equations

Journal of Differential Equations ◽

10.1016/j.jde.2006.08.021 ◽

2006 ◽

Vol 231 (2) ◽

pp. 714-754 ◽

Cited By ~ 45

Author(s):

A. Cheskidov ◽

C. Foias

Keyword(s):

Stokes Equations ◽

Global Attractors ◽

Navier Stokes ◽

Navier Stokes Equations

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Remarks on the navier-stokes equations on the two and three dimensional torus

Communications in Partial Differential Equations ◽

10.1080/03605309408821038 ◽

1994 ◽

Vol 19 (5-6) ◽

pp. 873-900 ◽

Cited By ~ 8

Author(s):

Vincent Xiaosong Liu

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Dimensional Torus ◽

Navier Stokes Equations

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Global attractors for the Navier–Stokes equations of three-dimensional compressible flow

Comptes Rendus de l Académie des Sciences - Series I - Mathematics ◽

10.1016/s0764-4442(00)00511-5 ◽

2000 ◽

Vol 331 (1) ◽

pp. 35-39 ◽

Cited By ~ 13

Author(s):

Eduard Feireisl

Keyword(s):

Compressible Flow ◽

Stokes Equations ◽

Three Dimensional ◽

Global Attractors ◽

Navier Stokes ◽

Navier Stokes Equations

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A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study

Il Nuovo Cimento B ◽

10.1007/bf02903283 ◽

1981 ◽

Vol 64 (2) ◽

pp. 207-220 ◽

Cited By ~ 8

Author(s):

P. M. Angelo ◽

G. Riela

Keyword(s):

Stokes Equations ◽

Numerical Study ◽

Navier Stokes ◽

Two Dimensional ◽

Dimensional Torus ◽

Navier Stokes Equations ◽

Mode Truncation

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A lower bound for the density of the steady Navier–Stokes equations

Applied Mathematics Letters ◽

10.1016/j.aml.2019.05.043 ◽

2019 ◽

Vol 98 ◽

pp. 88-94 ◽

Cited By ~ 1

Author(s):

Senming Chen ◽

Changjiang Zhu

Keyword(s):

Lower Bound ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations

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A five-mode truncation of the Navier-Stokes equations on a three-dimensional torus

Computational Mechanics ◽

10.1007/bf00280749 ◽

1988 ◽

Vol 3 (1) ◽

pp. 19-37 ◽

Cited By ~ 7

Author(s):

V. Franceschini ◽

G. Inglese ◽

C. Tebaldi

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Dimensional Torus ◽

Navier Stokes Equations ◽

Mode Truncation

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