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

Vincent Xiaosong Liu

doi:10.1007/bf02108078

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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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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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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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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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 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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Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2018279 ◽

2019 ◽

Vol 24 (8) ◽

pp. 3569-3590

Author(s):

Daniel Pardo ◽

◽

José Valero ◽

Ángel Giménez ◽

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Three Dimensional ◽

Global Attractors ◽

Navier Stokes ◽

Navier Stokes Equations

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Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Journal of the European Mathematical Society ◽

10.4171/jems/1162 ◽

2021 ◽

Author(s):

Tristan Buckmaster ◽

Maria Colombo ◽

Vlad Vicol

Keyword(s):

Hausdorff Dimension ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Singular Sets

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Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations

Mechanics: From Theory to Computation ◽

10.1007/978-1-4612-1246-1_16 ◽

2000 ◽

pp. 447-474 ◽

Cited By ~ 16

Author(s):

J. M. Ball

Keyword(s):

Stokes Equations ◽

Global Attractors ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Continuity Properties ◽

Generalized Semiflows

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On the Hausdorff dimension of singular sets for the Leray-α Navier-Stokes equations with fractional regularization

Dynamics of Partial Differential Equations ◽

10.4310/dpde.2012.v9.n3.a4 ◽

2012 ◽

Vol 9 (3) ◽

pp. 261-271 ◽

Cited By ~ 1

Author(s):

Hani Ali ◽

Zied Ammari

Keyword(s):

Hausdorff Dimension ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Singular Sets

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Navier-Stokes equations on thin $3$D domains. I. Global attractors and global regularity of solutions

Journal of the American Mathematical Society ◽

10.1090/s0894-0347-1993-1179539-4 ◽

1993 ◽

Vol 6 (3) ◽

pp. 503-503 ◽

Cited By ~ 3

Author(s):

Genevi{ève Raugel ◽

George R. Sell

Keyword(s):

Global Regularity ◽

Stokes Equations ◽

Global Attractors ◽

Regularity Of Solutions ◽

Navier Stokes ◽

Navier Stokes Equations

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