Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law

Esposito, R.; Guo, Yan; Kim, C.; Marra, R.

doi:10.1007/s00220-013-1766-2

Cited by 146 publications

(204 citation statements)

References 36 publications

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“…We know that the collision operator also has an equilibrating effect through the H-theorem. In a bounded domain, it is common to consider these two effects together (see [28,37,38] and references therein). However, they play different roles in the physical modelling.…”

Section: Kinetic Theory: Boundary Behaviourmentioning

confidence: 99%

Aspects of dissipation for compressible fluids and kinetic theory

Liu

2013

Phil. Trans. R. Soc. A.

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There are several types of dissipation—the viscosity and heat conductivity, the nonlinearity and the coupling of distinct characteristics—that can occur in the system of conservation laws. In addition to these corresponding types of dissipation, there are other consequences of the H-theorem and the boundary dissipative effects for the kinetic theory. We discuss these issues and raise questions.

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Section: Kinetic Theory: Boundary Behaviourmentioning

confidence: 99%

Aspects of dissipation for compressible fluids and kinetic theory

Liu

2013

Phil. Trans. R. Soc. A.

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“…Remark 3. There has been a lot of studies for Boltzmann equation in many aspects, the global solution [12, 11,1]; regularity estimate [14,13]; the steady solution [7,8,6]. So far we are only able to prove the local well-posedness with the C-L boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Cercignani-Lampis boundary in the Boltzmann theory

Chen¹

2020

Kinetic &Amp; Related Models

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The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the local well-posedness of the Boltzmann equation in bounded domain with the Cercignani-Lampis boundary condition, which describes the intermediate reflection law between diffuse reflection and specular reflection via two accommodation coefficients. We prove the local-in-time well-posedness of the equation by establishing an L ∞ estimate. In particular, for the L ∞ bound we develop a new decomposition on the boundary term combining with repeated interaction through the characteristic. Via this method, we construct a unique steady solution of the Boltzmann equation with constraints on the wall temperature and the accommodation coefficient.

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“…Gomeshi studied the existence of unique mild solutions under the condition that the Knudsen number is sufficiently large in [24]. For the related 3d problem near equilibrium, see [19,20].…”

Section: Introductionmentioning

confidence: 99%

Stationary Quantum BGK Model for Bosons and Fermions in a Bounded Interval

Bae

Yun

2019

J Stat Phys

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In this paper, we consider the existence problem for a stationary relaxational models of the quantum Boltzmann equation. More precisely, we establish the existence of mild solution to the fermionic or bosonic quantum BGK model in a slab with inflow boundary data. Unlike the classical case, it is necessary to verify that the quantum local equilibrium state is well-defined, and the transition from the non-condensed state to the condensated state (Bosons), or from the non-saturated state to the saturated state (Fermions) does not arise in our solution space. 3 5 , (1.4)

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Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law

Abstract: In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the following steady problem:

Cited by 146 publications

References 36 publications

Aspects of dissipation for compressible fluids and kinetic theory

Aspects of dissipation for compressible fluids and kinetic theory

Cercignani-Lampis boundary in the Boltzmann theory

Stationary Quantum BGK Model for Bosons and Fermions in a Bounded Interval

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