Stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system

Huang, Yongting; Liu, Hongxia

doi:10.1016/s0252-9602(18)30789-6

Cited by 5 publications

(4 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Luo-Yao-Zhu in [27] and Yao-Zhu in [40] established the stability of rarefaction wave for the isentropic Navier-Stokes-Maxwell equations and non-isentropic ones under small H 1 -initial perturbations, respectively. What' more, Huang-Liu in [14] consider the stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system, in which the model they consider is obviously different from ours in this paper, except for the similar dissipative term E + ub.…”

Section: The Problemmentioning

confidence: 79%

Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations

Yao

Zhu

2021

Preprint

View full text Add to dashboard Cite

We study the large-time asymptotic behavior of solutions toward the combination of a viscous contact wave with two rarefaction waves for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations through the Lorentz force (called the Navier-Stokes-Maxwell equations). It includes the electrodynamic effects into the dissipative structure of the hyperbolic-parabolic system and turns out to be more complicated than that in the simpler compressible Navier-Stokes equations. Based on a new observation of the specific structure of the Maxwell equations in the Lagrangian coordinates, we prove that this typical composite wave pattern is time-asymptotically stable for the Navier-Stokes-Maxwell equations under some smallness conditions on the initial perturbations and wave strength, and also under the assumption that the dielectric constant is bounded. The main result is proved by using elementary energy methods. This is the first result about the nonlinear stability of the combination of two different wave patterns for the compressible Navier-Stokes-Maxwell equations.

show abstract

Section: The Problemmentioning

confidence: 79%

Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations

Yao

Zhu

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…established the stability of rarefaction wave for the compressible isentropic and non-isentropic Navier-Stokes-Maxwell equations under suitable smallness conditions, respectively. Huang-Liu in[13] consider the stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system, in which the model they consider is obviously different from this in our paper, except for the similar dissipative term E + ub. Recently, Yao-Zhu in[49] study the asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations, which is the first result on the combination of two different wave patterns of this complex coupled model.…”

mentioning

confidence: 84%

Large-time behavior of solutions to the outflow problem for the compressible Navier-Stokes-Maxwell equations

Yao,

Zhu

2021

Preprint

View full text Add to dashboard Cite

We investigate the large-time behavior of solutions toward the combination of the boundary layer and 3-rarefaction waves to the outflow problem for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations through the Lorentz force (called the Navier-Stokes-Maxwell equations) on the half line R + . It includes the electrodynamic effects into the dissipative structure of the hyperbolic-parabolic system and turns out to be more complicated than that in the simpler compressible Navier-Stokes equations. We prove that this typical composite wave pattern is time-asymptotically stable with the composite boundary condition of the electromagnetic fields, under some smallness conditions and the assumption that the dielectric constant is bounded. This can be viewed as the first result about the nonlinear stability of the combination of two different wave patterns for the IBVP of the non-isentropic Navier-Stokes-Maxwell equations.

show abstract

“…Thirdly, in order to absorb some nonlinear bad terms by the single or the compound good term associated with the electromagnetic fields, we require a technical condition (1.29) that dielectric constant ε is bounded for some positive constantsC (depending only on |u ± | and θ − ), see estimates (2.23)-(2.26), (2.31) in Lemma 2.1 and estimates (2.40)-(2.43) in Lemma 2.2. We would like to mention that Huang-Liu in [10] consider the stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system. Here we should point out that, except for the similar dissipative term E + ub, the model we consider in this paper is obviously different from that in [10].…”

Section: Huancheng Yao Haiyan Yin and Changjiang Zhumentioning

confidence: 99%

“…We would like to mention that Huang-Liu in [10] consider the stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system. Here we should point out that, except for the similar dissipative term E + ub, the model we consider in this paper is obviously different from that in [10]. In contrast to the requirement of smallness of the profile |u r (x, t)| imposed in the proof of [10], in this paper, we require ε•max{|u − | , |u + |} to be small instead, which can not only contain but also extend the condition of [10] in some extent, see Remark 1 for details.…”

Section: Huancheng Yao Haiyan Yin and Changjiang Zhumentioning

confidence: 99%

Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations

Yao¹,

Yin²,

Zhu³

2021

CPAA

View full text Add to dashboard Cite

We study the large-time asymptotic behavior of solutions toward the rarefaction wave of the compressible non-isentropic Navier-Stokes equations coupling with Maxwell equations under some small perturbations of initial data and also under the assumption that the dielectric constant is bounded. For that, the dissipative structure of this hyperbolic-parabolic system is studied to include the effect of the electromagnetic field into the viscous fluid and turns out to be more complicated than that in the simpler compressible Navier-Stokes system. The proof of the main result is based on the elementary L 2 energy methods.

show abstract

Stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system

Cited by 5 publications

References 36 publications

Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations

Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations

Large-time behavior of solutions to the outflow problem for the compressible Navier-Stokes-Maxwell equations

Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations

Contact Info

Product

Resources

About