CONVERGENCE OF THE g-NAVIER-STOKES EQUATIONS

Roh, Jaiok

doi:10.11650/twjm/1500405278

Cited by 15 publications

(29 citation statements)

References 8 publications

(4 reference statements)

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“…Also Roh [36] has studied the above limit equation in the particular case where ∇g is small. Note also that the limit operator v → div h (gv) of the divergence already appeared in other works dealing with the Euler equations ( [19] for example).…”

Section: Vεmentioning

confidence: 99%

Navier-Stokes equations in thin 3D domains with Navier boundary conditions

Iftimie¹,

Raugel²,

Sell³

2007

Indiana Univ. Math. J.

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Abstract. We consider the Navier-Stokes equations on a thin domain of the form Ω ε = {x ∈ R 3 ; x 1 , x 2 ∈ (0, 1), 0 < x 3 < εg(x 1 , x 2 )} supplemented with the following mixed boundary conditions: periodic boundary conditions on the lateral boundary and Navier boundary conditions on the top and the bottom. Under the assumption that, 2} and similar assumptions on the forcing term, we show global existence of strong solutions; here u i 0 denotes the i-th component of the initial data u 0 and M is the average in the vertical direction, that is,Moreover, if the initial data, respectively the forcing term, converge to a bidimensional vector field, respectively forcing term, as ε → 0, we prove convergence to a solution of a limiting system which is a Navier-Stokes-like equation where the function g plays an important role. Finally, we compare the attractor of the Navier-Stokes equations with the one of the limiting equation.

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Section: Vεmentioning

confidence: 99%

Navier-Stokes equations in thin 3D domains with Navier boundary conditions

Iftimie¹,

Raugel²,

Sell³

2007

Indiana Univ. Math. J.

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“…The g-Stokes operator A g is an isomorphism from V g into V g , while B and R satisfy the following inequalities (see [1][2] and [24]):…”

Section: Preliminariesmentioning

confidence: 99%

“…In this paper, we consider the 2D nonautonomous g-Navier-Stokes (g-N-S) equations with linear dampness on an unbounded domain Ω ⊂ R 2 , which have the following form (see [1][2][3]):…”

Section: Introductionmentioning

confidence: 99%

Pullback attractor of 2D nonautonomous g-Navier-Stokes equations with linear dampness

Jin-ping

Hou

Wang

2011

Appl. Math. Mech.-Engl. Ed.

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The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness are investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.

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“…The 2D gNavier-Stokes equations arise in a natural way when we study the standard 3D problem in thin domains. We refer the reader to [17] for a derivation of the 2D g-Navier-Stokes equations from the 3D Navier-Stokes equations and a relationship between them. As mentioned in [17], good properties of the 2D g-Navier-Stokes equations can lead to an initial study of the Navier-Stokes equations on the thin 3D domain g = × (0, g).…”

Section: Introductionmentioning

confidence: 99%