The Cauchy problem for the BGK equation with an external force

Wei, Jinbo; Zhang, Xianwen

doi:10.1016/j.jmaa.2012.02.039

Cited by 14 publications

(6 citation statements)

References 22 publications

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“…The uniqueness problem in a weighted L ∞ setting was studied in [33]. These theories were then generalized to various directions such as the whole space case [27], L p setting [52], and the BGK models with external forces [10,46] or mean field effect [51]. Ukai studied the stationary problem in a bounded interval in [41].…”

Section: Introductionmentioning

confidence: 99%

Entropy production for ellipsoidal BGK model of the Boltzmann equation

Yun¹

2016

KRM

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The ellipsoidal BGK model (ES-BGK) is a generalized version of the BGK model of the Boltzmann equation designed to yield the correct Prandtl number in the Navier-Stokes limit. In this paper, we make two observations on the entropy production functional of the ES-BGK model. First, we show that the Cercignani type estimate holds for the ES-BGK model in the whole range of parameter −1/2 < ν < 1. Secondly, we observe that the ellipsoidal relaxation operator satisfies an unexpected sign-definite property. Some implications of these observations are also discussed.where ρ, U , T and Θ are macroscopic density, bulk velocity, temperature and stress tensor Θ respectively:

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Section: Introductionmentioning

confidence: 99%

Entropy production for ellipsoidal BGK model of the Boltzmann equation

Yun¹

2016

KRM

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“…Studies on Wigner-Poisson type equation can be found in [4,11,39,49,50,51,68,74]. We refer to [8,18,48,71,75,76,80,92,98,99,100,101,102,104,105] for mathematical results on classical BGK models. Nice survey on classical or quantum kinetic equations can be found in [15,16,17,33,84,85,87,90,91].…”

Section: )mentioning

confidence: 99%

Quantum BGK model near a global Fermi-Dirac distribution

Bae¹,

Yun²

2018

Preprint

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In this paper, we consider the existence and asymptotic behavior of the fermionic quantum BGK model, which is a relaxation model of the quantum Boltzmann equation for fermions. More precisely, we establish the existence of unique classical solutions and their exponentially fast stabilization when the initial data starts sufficiently close to a global Fermi-Dirac distribution. A key difficulty unobserved in the study of the classical BGK model is that we must verify that the equilibrium parameters is uniquely determined through a set of nonlinear equations in each iteration step.

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“…Global‐in‐time existence of weak solutions to the Cauchy problem of coupled with the Poisson potential field ( φ ( t , x )given by ) is shown in . In , some well‐posedness results were established for in presence of the general potential field. A long time behavior for the Equation coupled with an external confining potential was studied by Bosi and C

á

ceres in .…”

Section: Introductionmentioning

confidence: 99%

On the Cauchy problem for Wigner–Poisson–BGK equation in the Wiener algebra

Shen

2015

Math Methods in App Sciences

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In this paper, we prove the existence and uniqueness of the local mild solution to the Cauchy problem of the n-dimensional (n 3) Wigner-Poisson-BGK equation in the space of some integrable functions whose inverse Fourier transform are integrable. The main difficulties in establishing mild solution are to derive the boundedness and locally Lipschitz properties of the appropriate nonlinear terms in the Wiener algebra.

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The Cauchy problem for the BGK equation with an external force

Cited by 14 publications

References 22 publications

Entropy production for ellipsoidal BGK model of the Boltzmann equation

Entropy production for ellipsoidal BGK model of the Boltzmann equation

Quantum BGK model near a global Fermi-Dirac distribution

On the Cauchy problem for Wigner–Poisson–BGK equation in the Wiener algebra

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