On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains

Russell M. Brown; Peter A. Perry; Zhongwei Shen

doi:10.1512/iumj.2000.49.1603

On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains

Russell M. Brown, Peter A. Perry, Zhongwei Shen

Mathematics

Research output: Contribution to journal › Article › peer-review

30 Citations (SciVal)

Abstract

This paper concerns the two-dimensional Navier-Stokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞ (∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c₁G + c₂Re^3/2, where G is the Grashof number and Re the Reynolds number.

Original language	English
Pages (from-to)	81-112
Number of pages	32
Journal	Indiana University Mathematics Journal
Volume	49
Issue number	1
DOIs	https://doi.org/10.1512/iumj.2000.49.1603
State	Published - 2000

ASJC Scopus subject areas

Mathematics (all)

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10.1512/iumj.2000.49.1603

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title = "On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains",

abstract = "This paper concerns the two-dimensional Navier-Stokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞ (∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c1G + c2Re3/2, where G is the Grashof number and Re the Reynolds number.",

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AU - Perry, Peter A.

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N2 - This paper concerns the two-dimensional Navier-Stokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞ (∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c1G + c2Re3/2, where G is the Grashof number and Re the Reynolds number.

AB - This paper concerns the two-dimensional Navier-Stokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞ (∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c1G + c2Re3/2, where G is the Grashof number and Re the Reynolds number.

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On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains

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