Long time uniform stability for solutions of $n$-dimensional Navier-Stokes equations

Zhang, Linghai

doi:10.1090/qam/1686191

Cited by 3 publications

(4 citation statements)

References 23 publications

(15 reference statements)

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“…For any given divergence free initial data u 0 ∈ L 1 (R n ) ∩ H 2 (R n ), there exists at least a global weak solution u, such that (1 + t) 1+n/2 R n |u(x, t)| 2 dx C, with C being independent of time. See [2-6,19-32, 34-36,38,40] and [41][42][43][44]. Of course, many other people also established the decay estimates with optimal rate of decay for the global weak solutions of the Cauchy problems.…”

Section: Previous Resultsmentioning

confidence: 99%

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New results of general n-dimensional incompressible Navier–Stokes equations

Zhang

2008

Journal of Differential Equations

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Let u = u(x, t, u 0 ) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equationswhere the spatial dimension n 2, 0 ε 1 is a constant and β = (β 1 , β 2 , . . . , β n ) T ∈ R n is a constant vector. Note that if ε = 0 and β = 0, then the problem reduces to the traditional Navier-Stokes equations. Let the scalar functions φ ij ∈ C 2 (R n ) ∩ L 1 (R n ), ∂φ ij ∂x j

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Section: Previous Resultsmentioning

confidence: 99%

“…Suppose also that the global solutions of problems (1)-(2) satisfy u ∈ L q (R + , L p (R n )). See [2,3,39] and [43] for the same assumption.…”

Section: Hypothesesmentioning

confidence: 99%

New results of general n-dimensional incompressible Navier–Stokes equations

Zhang

2008

Journal of Differential Equations

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“…The problem of stability of solutions to – has been extensively studied by many authors (see, e.g., and the references therein). In the succeeding text, we briefly discuss the results on the stability, which are close to our work.…”

Section: Introductionmentioning

confidence: 99%

“…Let us emphasize that for solutions to (1.14)-(1.17), the Poincaré inequality holds. The problem of stability of solutions to (1.1)-(1.2) has been extensively studied by many authors (see, e.g., [19][20][21][22][23][24] and the references therein). In the succeeding text, we briefly discuss the results on the stability, which are close to our work.…”

Section: Introductionmentioning

confidence: 99%

Stability of two‐dimensional magnetohydrodynamic motions in the periodic case

Nowakowski

Zaja̧czkowski

2015

Math Methods in App Sciences

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We investigate the stability of two‐dimensional periodic solutions to magnetohydrodynamics equations in the class of three‐dimensional periodic solutions. We show the existence of global, strong three‐dimensional solutions to magnetohydrodynamics equations, which are close to two‐dimensional solutions. The advantage of our approach is that neither these solutions nor the external forces have to vanish at infinity. Copyright © 2015 John Wiley & Sons, Ltd.

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The exponential behavior and stabilizability of the stochastic 3D Navier–Stokes equations with damping

et al. 2019

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The stochastic 3D Navier–Stokes equation with damping driven by a multiplicative noise is considered in this paper. The stability of weak solutions to the stochastic 3D Navier–Stokes equations with damping is proved for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text]. The weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions are proved for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text]. The stabilization of these equations is obtained for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text].

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Long time uniform stability for solutions of $n$-dimensional Navier-Stokes equations

Cited by 3 publications

References 23 publications

New results of general n-dimensional incompressible Navier–Stokes equations

New results of general n-dimensional incompressible Navier–Stokes equations

Stability of two‐dimensional magnetohydrodynamic motions in the periodic case

The exponential behavior and stabilizability of the stochastic 3D Navier–Stokes equations with damping

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