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Xiao, Qingnong

doi:10.1016/j.jde.2015.04.031

Cited by 9 publications

(5 citation statements)

References 35 publications

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“…The investigations for the simpler model Vlasov-Poisson-Boltzmann system are more intensive, see [9,12,27,29] and reference therein. For the Landau equation coupled with the Maxwell system or Poisson equation, Guo [15] obtained the global classical solution for the classical Vlasov-Poisson-Landau equations in the torus, Duan [7] and Lei-Zhao [19] construct the global existence and large time behaviors of the classical Vlasov-Maxwell-Landau equations in the whole space, while the relativistic case are studied by Strain-Guo [26], Yang-Yu [31], Liu-Zhao [21] and many others [28].…”

Section: Previous Results and Our Approachmentioning

confidence: 99%

The relativistic Vlasov–Maxwell–Fokker–Planck system in the whole space

Liu

2020

Nonlinearity

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We are concerned with the Cauchy problem for the relativistic Vlasov-Maxwell-Fokker-Planck system in the whole space. For perturbative initial data with suitable regularity and integrability, we obtain the global classical solutions and the large time decay rates. For the proof, a new structure of the linearized relativistic Fokker-Planck operator is observed so that the coercivity estimates are established, crucial for the optimal large time decay rates is the pivotal Sobolev inequalities and interpolation inequalities as well as the structure of the coupled system. Moreover, it is shown that the energy without any weights decays in time with the polynomial rates varying directly with the derivatives of the solution, and the lower order derivatives of the solution except the magnetic field are further proved to decay faster than the optimal ones which coincide with the linearized equations without electro and magnetic fields, such a new phenomenon occurs only in the case of the relativistic Fokker-Planck model.

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Section: Previous Results and Our Approachmentioning

confidence: 99%

The relativistic Vlasov–Maxwell–Fokker–Planck system in the whole space

Liu

2020

Nonlinearity

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“…In this paper for nearby Maxwellian initital data the optimal large time decay rates were proven. Further see [38]. Then in 2015 Ha and Xiao in [21] established the L 2 stability of the relativistic Landau equation and the non-relativistic Landau equation.…”

Section: Resultsmentioning

confidence: 99%

Entropy dissipation estimates for the relativistic Landau equation, and applications

Strain

Tasković

2019

Journal of Functional Analysis

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In this paper we study the Cauchy problem for the spatially homogeneous relativistic Landau equation with Coulomb interactions. Despite it's physical importance, this equation has not received a lot of mathematical attention we think due to the extreme complexity of the relativistic structure of the kernel of the collision operator. In this paper we first largely decompose the structure of the relativistic Landau collision operator. After that we prove the global Entropy dissipation estimate. Then we prove the propagation of any polynomial moment for a weak solution. Lastly we prove the existence of a true weak solution for a large class of initial data.R.M.S. was partially supported by the NSF grants DMS-1500916 and DMS-1764177.

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“…We list some closely related to this article. For the r-VML system, we refer to Strain-Guo [83], Yu [99], Yang-Yu [98], Liu-Zhao [70] and Xiao [93]. For the r-LAN equation, we refer to Hsiao-Yu [53] and Yang-Yu [97].…”

Section: Background and Literaturementioning

confidence: 99%

Hilbert Expansion for the Relativistic Vlasov-Maxwell-Landau System

Ouyang¹,

Wu²,

Xiao³

2022

Preprint

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The two-species relativistic Vlasov-Maxwell-Landau system is the most fundamental and complete model describing the dynamics of a dilute plasma, in which particles interact through Coulombic collisions and through their self-consistent electromagnetic field. A rigorous derivation from the twospecies relativistic Vlasov-Maxwell-Landau system to the two-fluid relativistic Euler-Maxwell system is a longstanding major open problem in the kinetic theory. Thanks to recent works such as [32,46,45], we establish the global-in-time validity of Hilbert expansion for the relativistic Vlasov-Maxwell-Landau system and derive the limiting two-fluid relativistic Euler-Maxwell system as the Knudsen number goes to zero. Inspired by the weighted energy method in the pioneer work of Caflisch [13], our proof is based on a new time-dependent energy method, which is introduced in our first work [74] about the relativistic Landau equation case.

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Large-time behavior of the two-species relativistic Landau–Maxwell system inRx3

Cited by 9 publications

References 35 publications

The relativistic Vlasov–Maxwell–Fokker–Planck system in the whole space

The relativistic Vlasov–Maxwell–Fokker–Planck system in the whole space

Entropy dissipation estimates for the relativistic Landau equation, and applications

Hilbert Expansion for the Relativistic Vlasov-Maxwell-Landau System

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