Asymptotic behavior of global smooth solutions for full compressible Navier–Stokes–Maxwell equations

Feng, Yanghe; Peng, Yue‐Jun; Wang, Shu

doi:10.1016/j.nonrwa.2014.03.004

Cited by 24 publications

(14 citation statements)

References 21 publications

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“…Duan [1] and Feng et al [2] studied the compressible Navier-Stokes-Maxwell systems which take a little different form from the model considered in our paper and obtained the global well-posedness of the classic solution when the initial data are a small perturbation around some given constant steady state. For incompressible Navier-Stokes-Maxwell system, Masmoudi [15] and Kang and Lee [10] obtained the global well-posedness of the solutions in two-dimensional case.…”

Section: Assume Further That There Exists a Positive Constant α Such mentioning

confidence: 81%

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Uniform well-posedness and singular limits of the isentropic Navier–Stokes–Maxwell system in a bounded domain

Fan

Nakamura

2014

Z. Angew. Math. Phys.

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We prove the global-in-time and uniform-in-( 1 , 2 ) of strong solutions to the isentropic Navier-Stokes-Maxwell system in a bounded domain, when 1 is the Mach number, and 2 is the dielectric constant. Consequently, we obtain the convergences of compressible Navier-Stokes-Maxwell system to the incompressible Navier-Stokes-Maxwell system ( 1 → 0 and 2 fixed), the compressible magnetohydrodynamic equations ( 1 fixed and 2 → 0) or the incompressible magnetohydrodynamic equations ( 1 → 0 and 2 → 0) for well-prepared data.Mathematics Subject Classification. 76W05 · 35Q60 · 35B25.

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Section: Assume Further That There Exists a Positive Constant α Such mentioning

confidence: 81%

“…We first consider cases (1) and (2). In these situations, it is convenient to consider the flow with small density variation, i.e., ρ = 1 + 1 σ and we will take p (1) = 1.…”

Section: Introductionmentioning

confidence: 99%

Uniform well-posedness and singular limits of the isentropic Navier–Stokes–Maxwell system in a bounded domain

Fan

Nakamura

2014

Z. Angew. Math. Phys.

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“…Hong‐Hou‐Peng‐Zhu investigated the global existence of spherically symmetric classical solution to the Navier–Stokes–Maxwell system with large initial data and vacuum. Meanwhile, Feng‐Peng‐Wang considered the full compressible Navier–Stokes–Maxwell equations where the temperature equation takes the form of

θ_{t} + \frac{2}{3} u \cdot \nabla θ + u \cdot \nabla θ + (θ - 1) + \frac{1}{3} | u |^{2} = 0 .

They proved the global existence and large‐time behavior but without decay rate. Later, Wang‐Xu continued to study the full compressible Navier–Stokes–Maxwell system appeared in and obtained the time‐decay rate of the global smooth solutions based on a detailed analysis to the Green's function of the linearized system and some elaborate energy estimates.…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, Feng-Peng-Wang [7] considered the full compressible Navier-Stokes-Maxwell equations where the temperature equation takes the form ofThey proved the global existence and large-time behavior but without decay rate. Later, Wang-Xu [8] continued to study the full compressible Navier-Stokes-Maxwell system appeared in [7] and obtained the time-decay rate of the global smooth solutions based on a detailed analysis to the Green's function of the linearized system and some elaborate energy estimates. Another interesting model is Navier-Stokes-Poisson system when the magnetic field is absent.…”

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confidence: 99%

Large time behavior for the non‐isentropic Navier–Stokes–Maxwell system

Liu

2016

Math Methods in App Sciences

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Communicated by C. MiaoIn this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near constant steady states is established, and the time-decay rates of perturbed solutions are obtained. The proof for existence is due to the classical energy method, and the investigation of large-time behavior is based on the linearized analysis of the non-isentropic Navier-Stokes-Poisson equations and the electromagnetic part for the linearized isentropic NavierStokes-Maxwell equations. In the meantime, the time-decay rates obtained by Zhang, Li, and Zhu [J. Differential Equations, 250(2011), 866-891] for the linearized non-isentropic Navier-Stokes-Poisson equations are improved.

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“…For an overview, see, for example, [7][8][9][10][11][12][13][14] and the references therein. For some other systems, more details can be referred to [15][16][17][18][19][20].…”

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confidence: 99%

Decay of the nematic liquid crystal system

Wei

Yao

2015

Math. Meth. Appl. Sci.

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In this paper, we study the time‐decay rates of the solution to the Cauchy problem for a nematic liquid crystals system via a refined pure energy method. In particular, the optimal decay rates of the higher‐order spatial derivatives of the solution are obtained. The trueḢ−s()0≤s≤12 negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. Copyright © 2015 John Wiley & Sons, Ltd.

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Asymptotic behavior of global smooth solutions for full compressible Navier–Stokes–Maxwell equations

Cited by 24 publications

References 21 publications

Uniform well-posedness and singular limits of the isentropic Navier–Stokes–Maxwell system in a bounded domain

Uniform well-posedness and singular limits of the isentropic Navier–Stokes–Maxwell system in a bounded domain

Large time behavior for the non‐isentropic Navier–Stokes–Maxwell system

Decay of the nematic liquid crystal system

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