The Relativistic Quantum Boltzmann Equation Near Equilibrium

Bae, Gi-Chan; Jang, Jin Woo; Yun, Seok-Bae

doi:10.1007/s00205-021-01643-6

Cited by 14 publications

(9 citation statements)

References 67 publications

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“…When we are preparing this work, we are aware of the recent preprint by Bae-Jang-Yun [6] on the relativistic quantum Boltzmann equation. They used the nonlinear energy method similar to ours.…”

Section: Motivation and Previous Resultsmentioning

confidence: 99%

“…• More importantly, the nonlinear estimates are different. While in [6] they can bound the nonlinear term in the relativistic case without using L ∞ bounds in velocity, such an estimate is absent in the non-relativistic scenario. Therefore, we must take velocity derivatives and use Sobolev embedding, which introduces a lot of technical difficulties.…”

Section: Motivation and Previous Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On the Quantum Boltzmann Equation near Maxwellian and Vacuum

Ouyang¹,

Wu²

2021

Preprint

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We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and vacuum. This work is a generalization and adaptation of the classical Boltzmann theory. Our main contribution is a detailed analysis of the nonlinear operator Q in the quantum context. This is the first piece of a long-term project on the quantum kinetic equations.

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Section: Motivation and Previous Resultsmentioning

confidence: 99%

Section: Motivation and Previous Resultsmentioning

confidence: 99%

On the Quantum Boltzmann Equation near Maxwellian and Vacuum

Ouyang¹,

Wu²

2021

Preprint

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“…In terms of mathematical methods, this article is closer to [5], [44] and [27] since all of these works fall into the close-to-equilibrium framework well established for the classical Boltzmann equation. There are many great works that contribute to this mathematically satisfactory theory for global well-posedness of the classical Boltzmann equation.…”

Section: Introductionmentioning

confidence: 97%

“…Note that all the above results on BBE equations are obtained in the homogeneous case. In the inhomogeneous case, there are at least two recent results: Bae-Jang-Yun [5] and Ouyang-Wu [44]. These two works have different focuses and will be revisited later.…”

Section: Introductionmentioning

confidence: 99%

Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials

Zhou¹

2022

Preprint

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We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global well-posedness of the corresponding Cauchy problem is proved in a periodic box near equilibrium for initial data satisfying high temperature condition. Contents 1. Introduction 1 2. Linear operator estimate 12 3. Bilinear operator estimate 20 4. Trilinear operator estimate 31 5. Commutator estimate and weighted energy estimate 37 6. Local well-posedness 47 7. A priori estimate and global well-posedness 53 8. Appendix 60 References 69

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“…Recently, using the nonlinear energy method and mild formulation, Ouyang-Wu [25] established the global well-posedness for the non-homogeneous quantum Boltzmann equation (1.1). We refer the interested readers to [1] for the global existence and large time behavior of the relativistic quantum Boltzmann equation. For the homogeneous quantum Boltzmann equation, we refer to Lu [20,21,19,18], Lu-Wennberg [22], Lu-Zhang [23] and Briant-Einav [2].…”

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confidence: 99%

Global existence and large time behavior of the quantum Boltzmann equation with small relative entropy

Wang

Xiao

Zhang

2023

KRM

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<p style='text-indent:20px;'>In this paper, we study the global well-posedness of the non-relativistic quantum Boltzmann equation with initial data of small relative entropy. For a class of initial data which are allowed to have arbitrary bounded amplitude and even contain vacuum, we establish the global existence and uniqueness of the mild solutions to the quantum Boltzmann equation in the torus <inline-formula><tex-math id="M1">\begin{document}$ x\in\mathbb T^3 $\end{document}</tex-math></inline-formula>. The exponential time decay rate is also obtained in the <inline-formula><tex-math id="M2">\begin{document}$ L^{\infty}_{x, v} $\end{document}</tex-math></inline-formula>-norm.</p>

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The Relativistic Quantum Boltzmann Equation Near Equilibrium

Cited by 14 publications

References 67 publications

On the Quantum Boltzmann Equation near Maxwellian and Vacuum

On the Quantum Boltzmann Equation near Maxwellian and Vacuum

Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials

Global existence and large time behavior of the quantum Boltzmann equation with small relative entropy

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