Global spherically symmetric classical solution to the Navier-Stokes-Maxwell system with large initial data and vacuum

Hong, Guangyi; Hou, Xiaojuan; Peng, Hongyun; Zhu, Changjiang

doi:10.1007/s11425-014-4896-x

Cited by 9 publications

(16 citation statements)

References 25 publications

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“…By Cauchy's inequality, this together with (10) gives (12) (14) with s = 1/2 that the following decay result holds:…”

Section: Proof Of Theoremsmentioning

confidence: 97%

“…However, we are not able to prove them for all s ∈ [0, 3/2) at this moment. We must distinguish the arguments by the value of s. First, for s ∈ (0, 1/2], integrating (68) in time, by (10) we obtain that for s ∈…”

Section: Proof Of Theoremsmentioning

confidence: 99%

“…For the three-dimensional smooth solutions to the compressible Navier-Stokes-Maxwell equations under the assumption of initial small amplitude near a constant equilibrium state, Duan [2] proved the global existence and asymptotic behavior of smooth solutions by using Green's function argument for isentropic case, while Feng-Peng-Wang [5] established the large-time behavior of global smooth solutions by using careful energy estimates and the techniques of symmetrizer for the non-isentropic case. Hong et al [10] considered the initial boundary value problem to the isentropic Navier-Stokes-Maxwell system with large initial data and initial vacuum in a bounded annulus Ω of R 3 and obtained the global spherically symmetric classical solutions. For incompressible Navier-Stokes-Maxwell equations, we can refer to [12,4] for the existence of local unique solutions, to [11,6] for mild solutions, and to [17] for global strong solutions.…”

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confidence: 99%

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Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$

Tan¹,

Tong²

2018

Kinetic &Amp; Related Models

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The compressible non-isentropic Navier-Stokes-Maxwell system is investigated in R 3 and the global existence and large time behavior of solutions are established by pure energy method provided the initial perturbation around a constant state is small enough. We first construct the global unique solution under the assumption that the H 3 norm of the initial data is small, but the higher order derivatives can be arbitrarily large. If further the initial data belongs toḢ −s (0 ≤ s < 3/2) orḂ −s 2,∞ (0 < s ≤ 3/2), by a regularity interpolation trick, we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the L p-L 2 (1 ≤ p ≤ 2) type of the decay rates follows without requiring that the L p norm of initial data is small.

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“…By Cauchy's inequality, this together with (10) gives (12) (14) with s = 1/2 that the following decay result holds:…”

Section: Proof Of Theoremsmentioning

confidence: 97%

Section: Proof Of Theoremsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$

Tan¹,

Tong²

2018

Kinetic &Amp; Related Models

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“…For instance, Hou‐Yao‐Zhu established the global existence and uniqueness of strong solutions to the one‐dimensional compressible Navier–Stokes–Maxwell system with large initial data for the initial boundary value problem. 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.…”

Section: Introductionmentioning

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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“…The global existence and large time behavior of this model have been studied by Duan [5]. The global existence of spherical symmetric classical solution to the Navier-Stokes-Maxwell system is obtained with large initial data and vacuum [10]. For the bipolar compressible Navier-Stokes-Maxwell system in R 3 , under the assumption that the initial values are close to a equilibrium solutions, asymptotic behavior of global smooth solutions to the Cauchy problem is proved in [9] without decay rate.…”

mentioning

confidence: 99%

Local well-posedness of the full compressible Navier-Stokes-Maxwell system with vacuum

Fan¹,

Jia²

2018

Kinetic &Amp; Related Models

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Global spherically symmetric classical solution to the Navier-Stokes-Maxwell system with large initial data and vacuum

Cited by 9 publications

References 25 publications

Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$

Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$

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

Local well-posedness of the full compressible Navier-Stokes-Maxwell system with vacuum

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