Finite Speed of Propagation of the Relativistic Landau and Boltzmann Equations

Lyu, Ming-Jiea; Sun, Baoyan; Wu, Kaidi

doi:10.1007/s10955-021-02850-x

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…For the investigation of the relativistic Landau/Fokker-Planck equation (including physical models and global well-posedness), we refer to Danielewicz [9], Hsiao-Yu [25], Lemou [34], Luo-Yu [37], Lyu-Sun-Wu [38], Strain-Tasković [46] and Yang-Yu [50]. We also mention the recent works about the relativistic Boltzmann equation without angular cutoff in Jang-Strain [30,29].…”

Section: Background and Literature Reviewmentioning

confidence: 99%

Hilbert Expansion for the Relativistic Landau Equation

Ouyang¹,

Wu²,

Xiao³

2022

Preprint

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In this paper, we study the local-in-time validity of the Hilbert expansion for the relativistic Landau equation. We justify that solutions of the relativistic Landau equation converge to small classical solutions of the limiting relativistic Euler equations as the Knudsen number shrinks to zero in a weighted Sobolev space. The key difficulty comes from the temporal and spatial derivatives of the local Maxwellian, which produce momentum growth terms and are uncontrollable by the standard L 2 -based energy and dissipation. We introduce novel time-dependent weight functions to generate additional dissipation terms to suppress the large momentum. The argument relies on a hierarchy of energy-dissipation structures with or without weights. As far as the authors are aware of, this is the first result of the Hilbert expansion for the Landau-type equation.

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Section: Background and Literature Reviewmentioning

confidence: 99%

Hilbert Expansion for the Relativistic Landau Equation

Ouyang¹,

Wu²,

Xiao³

2022

Preprint

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Propagation phenomena of the solution for the relativistic BGK model

Sun

2023

Journal of Mathematical Physics

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In this paper, we recognize the finite propagation speed of the solution for the relativistic Bhatnagar-Gross-Krook model of the Marle-type near equilibrium regime in the whole space [Formula: see text]. The global solutions vanish outside a modified line cone ⟨ x⟩ = aMt with a, M > 1. Moreover, one can see that the slope of the modified line cone aM can be as close as to the maximum speed of the relativistic transport part. This means that the propagation speed is optimal.

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Finite Speed of Propagation of the Relativistic Landau and Boltzmann Equations

Cited by 2 publications

References 28 publications

Hilbert Expansion for the Relativistic Landau Equation

Hilbert Expansion for the Relativistic Landau Equation

Propagation phenomena of the solution for the relativistic BGK model

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