Space-time behavior of the solution to the Boltzmann equation with soft potentials

Lin, Yu-Chu; Lyu, Ming-Jiea; Wang, Haitao; Wu, Kaidi

doi:10.1016/j.jde.2022.03.024

Cited by 6 publications

(2 citation statements)

References 27 publications

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“…The pointwise behavior of the Green function of the Boltzmann equation for hard sphere was first verified in [22,23,24]. Later, the pointwise behavior of Green function of the Boltzmann equation for hard, Maxwellian and soft potentials was studied in [18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

Li¹,

Zhong²

2023

KRM

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The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed √ a 2 + b 2 at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function.

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Section: Introductionmentioning

confidence: 99%

Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

Li¹,

Zhong²

2023

KRM

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“…In [26], they constructed L 2 ∩ L ∞ β solution to the Boltzmann equation in the whole space using Duhamel's principle and the spectral theory. Recently, authors in [23] provide new analysis to derive L ∞ estimate rather than using Green function and Duhamel's principle. In addition, there are lots of references [2,4,5,6,8,18,19,22,24], where the low regularity solutions were studied for the cut-off type Boltzmann equation.…”

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confidence: 99%

On <inline-formula><tex-math id="M1">$ C^{2} $</tex-math></inline-formula> solution of the free-transport equation in a disk

Lee

2023

KRM

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<p style='text-indent:20px;'>The free transport operator of probability density function <inline-formula><tex-math id="M2">\begin{document}$ f(t, x, v) $\end{document}</tex-math></inline-formula> is one the most fundamental operator which is widely used in many areas of PDE theory including kinetic theory, in particular. When it comes to general boundary problems in kinetic theory, however, it is well-known that high order regularity is very hard to obtain in general. In this paper, we study the free transport equation in a disk with the specular reflection boundary condition. We obtain initial-boundary compatibility conditions for <inline-formula><tex-math id="M3">\begin{document}$ C^{1}_{t, x, v} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ C^{2}_{t, x, v} $\end{document}</tex-math></inline-formula> regularity of the solution. We also provide regularity estimates.</p>

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A Revisit of the Velocity Averaging Lemma: On the Regularity of Stationary Boltzmann Equation in a Bounded Convex Domain

Chen

Chuang²,

Hsia³

et al. 2022

J Stat Phys

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Space-time behavior of the solution to the Boltzmann equation with soft potentials

Cited by 6 publications

References 27 publications

Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

On <inline-formula><tex-math id="M1">$ C^{2} $</tex-math></inline-formula> solution of the free-transport equation in a disk

A Revisit of the Velocity Averaging Lemma: On the Regularity of Stationary Boltzmann Equation in a Bounded Convex Domain

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