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

Fan, Jishan; Li, Fucai; Nakamura, Gen

doi:10.1007/s00033-014-0484-8

Cited by 17 publications

(6 citation statements)

References 19 publications

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“…In this section we shall prove Theorem 1.1 by combining the ideas developed in [1,3,4,11]. First, by taking the similar arguments to that [1,11], we know that in order to prove (1.19), it suffices to show the following inequality…”

Section: Proof Of Theorem 11mentioning

confidence: 96%

See 1 more Smart Citation

Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

Fan¹,

Li²,

Nakamura³

2016

KRM

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Section: Proof Of Theorem 11mentioning

confidence: 96%

“…Because the local existence for the problem (1.8)-(1.14) with fixed ǫ > 0 is essential similar to that in [13], we only need to prove (2.1). We will use the methods developed in [3,4].…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

Fan¹,

Li²,

Nakamura³

2016

KRM

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“…Fan et al. [8] proved the global‐in‐time and uniform‐in‐

(\epsilon _1,\epsilon _2)

of strong solutions to the isentropic Navier‐Stokes‐Maxwell system with constant viscosity in a bounded domain, they also showed the convergence of the compressible Navier‐Stokes‐Maxwell equations to incompressible Navier‐Stokes‐Maxwell equations. The existence of global spherically symmetric classical solution to the compressible Navier‐Stokes‐Maxwell equations was obtained by Hong et al.…”

Section: Introductionmentioning

confidence: 99%

Global weak solution to the degenerate quantum Navier‐Stokes‐Maxwell equations with damping term

Wang

Guo

2022

Z Angew Math Mech

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In this paper we investigate the global existence of the finite energy weak solution to the isentropic quantum Navier-Stokes-Maxwell equations with density-dependent viscosity and the damping term in three-dimensional periodic domain. This model is composed of the isentropic compressible Navier-Stokes-Maxwell equation with density-dependent viscosity, the quantum Bohm potential and a damping term. This model can be used to describe the motion of the particle in the plasma under the electric-magnetic field. The main techniques are the Faedo-Galerkin method, some imbedding inequalities and some compactness theorems.

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“…Jiang and Li studied the vanishing limit of dielectric constant

ϵ_{1}

. Fan et al considered the vanishing limits of dielectric constant

ϵ_{1}

or the Mach number

ϵ_{2}

. Chen et al and Mi and Gao established the long‐time asymptotic behavior of the smooth solutions.…”

Section: Introductionmentioning

confidence: 99%

Local well‐posedness of the isentropic Navier‐Stokes‐Maxwell system with vacuum

Fan

Jing

Nakamura

et al. 2020

Math Methods in App Sciences

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In this work, we prove the local well-posedness of strong solutions to the isentropic compressible Navier-Stokes-Maxwell system with vacuum in a smooth, simply connected and bounded domain Ω ⊂ R. KEYWORDS isentropic, LWP, Navier-Stokes-Maxwell, vacuum MSC CLASSIFICATION 35Q30; 35Q35; 35B25 Math Meth Appl Sci. 2020;43:5357-5368. wileyonlinelibrary.com/journal/mma © 2020 John Wiley & Sons, Ltd. 5357 FAN ET AL.We will assume the following compatibility condition:This model is a coupled system of equations consisting the Lorentz force in the fluid equation and the electric current in the Maxwell equations. Equation (1.3) is called the Ampere-Maxwell equation, which has essential different structure with the majority of magnetohydrodynamics models. According to classical quasi-neutrality assumption, most of mathematicians consider the Maxwell's system as a parabolic equation for the magnetic field b. However, we keep the hyperbolic nature of Maxwell equation, which brings difficulty to analyze the existence. Regarding the incompressible case, the existence, regularity criteria, and long-time behavior has been studied by several studies. [3][4][5][6] To the authors' best knowledge, there are few results at compressible case. When = 0, Equations (1.1) and (1.2) reduce to the well-known isentropic compressible Navier-Stokes system, Gong et al 7 and Huang 8 showed the local well-posedness of strong solutions without Equation (1.8).When inf 0 > 0, the problem has received many studies. Jiang and Li 9-11 studied the vanishing limit of dielectric constant 1 . Fan et al [12][13][14] considered the vanishing limits of dielectric constant 1 or the Mach number 2 . Chen et al 15 and Mi and Gao 16 established the long-time asymptotic behavior of the smooth solutions.When inf 0 = 0, Fan and Jia 17 showed the local-posedness of strong solutions under Equation (1.8). The aim of this paper is to prove a similar result without Equation (1.8). We will proveThen the problem has a unique local strong solution ( , u, E, b) satisfyingHow to cite this article: Fan J, Jing L, Nakamura G, Tang T. Local well-posedness of the isentropic Navier-Stokes-Maxwell system with vacuum. Math Meth Appl Sci. 2020;43:5357-5368. https://doi.

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

Cited by 17 publications

References 19 publications

Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

Global weak solution to the degenerate quantum Navier‐Stokes‐Maxwell equations with damping term

Local well‐posedness of the isentropic Navier‐Stokes‐Maxwell system with vacuum

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