Global existence and exponential stability of solutions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>for the compressible Navier–Stokes equations with the cylinder symmetry

Qin, Yuming; Jiang, Limin

doi:10.1016/j.jde.2010.05.019

Cited by 16 publications

(2 citation statements)

References 26 publications

(41 reference statements)

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“…Remark 1.4. The similar results holds when the initial data is in [26]; The same conclusions as in Theorem 1.1 hold for the p-th power Newtonian fluid where the pressure P = Rρ p θ, see [2].…”

Section: Xinhua Zhao and Zilai LIsupporting

confidence: 71%

“…In fact, the global solutions converge exponentially to constant states as time tends to infinity. This argument has been applied to the case of spherically symmetric solutions and cylindrically symmetric solutions with large initial data [10,25,26]. Recently, Cui and Yao [2] got the exponential decay for the global spherically or cylindrically symmetric solutions with large initial data for the compressible p-th power Newtonian fluid.…”

Section: Xinhua Zhao and Zilai LImentioning

confidence: 99%

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Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations with large initial data

Zhao¹,

Li²

2020

Communications on Pure &Amp; Applied Analysis

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In this paper, we study the asymptotic behavior of global spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations for the viscous heat conducting ideal polytropic gas flow with large initial data in H 1 , when the heat conductivity coefficient depends on the temperature, practically, κ(θ) =κ 1 +κ 2 θ q where constantsκ 1 > 0,κ 2 > 0 and q > 0 (as to the case ofκ 1 = 0, please refer to the Appendix). In addition, the exponential decay rate of solutions toward to the constant state as time tends to infinity for the initial boundary value problem in bounded domain is obtained. The mass density and temperature are proved to be pointwise bounded from below and above, independent of time although strong nonlinearity in heat diffusion. The analysis is based on some delicate uniform energy estimates independent of time.

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Section: Xinhua Zhao and Zilai LIsupporting

confidence: 71%

Section: Xinhua Zhao and Zilai LImentioning

confidence: 99%

Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations with large initial data

Zhao¹,

Li²

2020

Communications on Pure &Amp; Applied Analysis

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3‐D flow of a compressible viscous micropolar fluid with cylindrical symmetry: uniqueness of a generalized solution

Mujaković

Simčić

Črnjarić-Žic

2016

Math Methods in App Sciences

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In this paper, we consider a nonstationary 3‐D flow of a compressible viscous and heat‐conducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The fluid domain is a subset of R3 bounded with two coaxial cylinders that present solid thermoinsulated walls. The mathematical model is set up in Lagrangian description. If we assume that the initial mass density, temperature, as well as the velocity and microrotation vectors are smooth enough cylindrically symmetric functions, then our problem has a generalized cylindrically symmetric solution for a sufficiently small time interval. Here, we prove the uniqueness of this solution. Copyright © 2016 John Wiley & Sons, Ltd.

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Large‐time behavior of solutions to the 3‐D flow of a compressible viscous micropolar fluid with cylindrical symmetry

Huang

Črnjarić-Žic

2018

Math Methods in App Sciences

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In this paper, we study the asymptotic behavior of global weak solutions in H1 to the problem that describes compressible viscous and heat‐conducting micropolar fluid flow in a three‐dimensional domain bounded by two circular, coaxial, and infinite cylinders that present the solid thermoinsulated walls. In the thermodynamical sense, the fluid is perfect and polytropic. We prove that the global weak solution exists and converges to a steady state as time goes to infinity. We have been working under the assumption that the initial data are cylindrically symmetric and the initial total energy is sufficiently small.

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Global existence and exponential stability of solutions inH4for the compressible Navier–Stokes equations with the cylinder symmetry

Cited by 16 publications

References 26 publications

Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations with large initial data

Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations with large initial data

3‐D flow of a compressible viscous micropolar fluid with cylindrical symmetry: uniqueness of a generalized solution

Large‐time behavior of solutions to the 3‐D flow of a compressible viscous micropolar fluid with cylindrical symmetry

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