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Byung-Hoon Hwang

Publications and source records attributed to Byung-Hoon Hwang.

17 recordsLinked to original sources
arXiv2026

Global mild solutions and the semiclassical limit for the Fermi--Dirac BGK model

We prove global existence of mild solutions to the spatially inhomogeneous Fermi--Dirac BGK equation for arbitrary-size Pauli-admissible initial data with finite mass and kinetic energy, allowing both vacuum and locally saturated zero-temperature states. The construction relies on a moment-compatible regularization of the local equilibrium that preserves the Pauli bound and uniform moment control while remaining consistent up to the saturation boundary. The solutions satisfy mass, momentum, and energy conservation and, under an additional finite spatial second-moment assumption, an entropy-gap H-theorem on the full Pauli interval. Under uniform moment and entropy bounds, we further prove that, after extraction of a subsequence, quantum mild solutions converge strongly in phase space, uniformly on bounded time intervals, to a mild solution of the classical BGK equation.

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arXiv2026

Incompressible Navier-Stokes-Fourier limit from a nonlinear quantum Fokker-Planck equation

We derive the incompressible Navier-Stokes-Fourier limit from a nonlinear quantum Fokker-Planck equation with Bose-Einstein or Fermi-Dirac statistics. The model has a self-consistent collision structure, with the local density acting as the collision frequency and the bulk velocity and temperature determined by nonlinear quantum-weighted moments of the distribution. We work near a global quantum equilibrium under the diffusive scaling and keep the quantum parameter fixed. Uniform estimates with respect to the Knudsen number yield strong microscopic relaxation and identify the limiting infinitesimal quantum equilibrium. Using the local conservation laws, we prove the incompressibility condition, the Boussinesq relation, and strong compactness of the divergence-free velocity component and a quantum-adapted thermal mode, while the acoustic modes vanish locally by a dispersive estimate. The limiting viscous stress tensor and heat flux are identified by solving auxiliary equations for the linearized quantum Fokker-Planck operator and by expanding the local quantum equilibrium manifold. The resulting incompressible Navier-Stokes-Fourier system retains the effect of quantum statistics through its normalization constants and transport coefficients.

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arXiv2026

Nonlinear quantum Fokker-Planck equation near equilibrium

We investigate a nonlinear quantum Fokker--Planck equation with self-consistent collision frequency, bulk velocity, and temperature. In contrast to quantum Fokker--Planck equations with prescribed diffusion and friction coefficients, the macroscopic quantities are nonlinear functionals of the distribution function. The equation preserves mass, momentum, and kinetic energy, admits a quantum entropy dissipation structure, and propagates the Pauli admissible range in the fermionic case. Its collision operator is also formally connected to the quantum Landau equation. For the Cauchy problem in the three-dimensional whole space, we prove the global-in-time existence and uniqueness of strong solutions near a global quantum equilibrium. The proof is based on a perturbative macro--micro energy method that combines microscopic coercivity, estimates for nonlinear velocity moments, and a macroscopic dissipation argument. We further establish the propagation of nonnegativity and the fermionic Pauli upper bound. Under an additional negative Sobolev assumption on the initial perturbation, we obtain algebraic decay rates toward equilibrium.

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arXiv2025

Relativistic BGK model for reactive gas mixtures

We propose a BGK-type kinetic model for relativistic reactive gas mixtures. This model serves as a computationally tractable yet physically consistent alternative to the corresponding Boltzmann equation. The relaxation operator is constructed to ensure that the model correctly satisfies the conservation laws and relaxes to the proper equilibrium: a Jüttner distribution characterized by a common temperature, velocity, and chemical potentials that obey the law of mass action. Furthermore, we prove that the model satisfies an H-theorem with the same entropy functional as the original Boltzmann equation. Finally, numerical simulations are presented, which confirm that the model preserves the conserved quantities and exhibits entropy decay towards the proper Jüttner equilibrium.

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arXiv2025

From kinetic mixtures to compressible two-phase flow: A BGK-type model and rigorous derivation

We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is constructed by solving an entropy minimization problem under moments constraints. Starting from this model, we derive the compressible two-phase Euler equations via a formal Chapman--Enskog expansion and identify dissipative corrections of Navier--Stokes type. We then rigorously justify the Euler limit using the relative entropy method, establishing quantitative convergence estimates under appropriate regularity assumptions. Finally, we present numerical experiments based on an implicit-explicit Runge--Kutta method, which confirm the asymptotic preserving property and demonstrate the convergence from the BGK model to the isentropic two-phase Euler system in the hydrodynamic regime.

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arXiv2025

Relativistic BGK model of Marle for polyatomic gases near equilibrium

In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in [Ann. Phys. 377 (2017) 414--445] to the relativistic BGK model proposed by Marle. We present the perturbed Marle model around the generalized Jüttner distribution and investigate the properties of the linear operator. Then we prove the global existence and large-time behavior of classical solutions when the initial data is sufficiently close to a global equilibrium.

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arXiv2024

Global existence of weak solutions to the nonlinear Vlasov-Fokker-Planck equation

In this paper, we study the nonlinear Vlasov-Fokker-Planck equation with fixed collision frequency. We establish the global-in-time existence of weak solutions to the equation with large initial data. Moreover, we show that our solution satisfies the conservation laws of mass, momentum, and energy, and Boltzmann's $H$-theorem.

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arXiv2024

Stationary solutions to the relativistic BGK model for gas mixtures in a slab

In a recent paper [16], the authors proposed a BGK model for relativistic gas mixtures based on the Marle-type approximation, which satisfies the fundamental kinetic properties: non-negativity of distribution functions, conservation laws, H-theorem, and indifferentiability principle. In this paper, we are concerned with the stationary problems to the relativistic BGK model for gas mixtures in slab geometry. We establish the existence of a unique mild solution with the fixed inflow boundary data when the collision frequencies for each species are sufficiently small.

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arXiv2024

Classical solutions to a BGK-type model relaxing to the isentropic gas dynamics

In this paper, we consider a BGK-type kinetic model relaxing to the isentropic gas dynamics in the hydrodynamic limit. We introduce a linearization of the equation around the global equilibrium. Then we prove the global existence of classical solutions with an exponential convergence rate toward the equilibrium state in the periodic domain when the initial data is a small perturbation of the global equilibrium.

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arXiv2024

Determination of equilibrium parameters of the Marle model for polyatomic gases

The BGK model is a relaxation-time approximation of the celebrated Boltzmann equation, and the Marle model is a direct extension of the BGK model in a relativistic framework. In this paper, we introduce the Marle model for polyatomic gases based on the Jüttner distribution devised in [Ann. Phys., 377, (2017), 414--445], and show the existence of a unique set of equilibrium parameters of the Jüttner distribution.

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arXiv2023

Relativistic BGK model for gas mixtures

Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results %\cite{Kremer,Kremer3,KP} in which such relativistic BGK models for gas mixture are employed to compute transport coefficients. However, to the best knowledge of authors, relativistic BGK models for gas mixtures with complete presentation of the relaxation operators are missing in the literature. In this paper, we fill this gap by suggesting a BGK model for relativistic gas mixtures for which the existence of each equilibrium coefficients in the relaxation operator is rigorously guaranteed in a way that all the essential physical properties are satisfied such as the conservation laws, the H-theorem, the capturing of the correct equilibrium state, the indifferentiability principle, and the recovery of the classical BGK model in the Newtonian limit.

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arXiv2023

Global existence of weak solutions to a BGK model relaxing to the barotropic Euler equations

We establish the global-in-time existence of weak solutions to a variant of the BGK model proposed by Bouchut [J. Stat. Phys., 95, (1999), 113--170] which leads to the barotropic Euler equations in the hydrodynamic limit. Our existence theory makes the quantified estimates of hydrodynamic limit from the BGK-type equations to the multi-dimensional barotropic Euler system discussed by Berthelin and Vasseur [SIAM J. Math. Anal., 36, (2005), 1807--1835] completely rigorous.

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arXiv2023

From BGK-alignment model to the pressured Euler-alignment system with singular communication weights

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights $ϕ_α(x) = |x|^{-α}$ for some $α> 0$. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure $p(ρ) = ρ^γ$, $γ= 1 + \frac2d$ from that kinetic equation.

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arXiv2021

On a relativistic BGK model for polyatomic gases near equilibrium

Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of the Anderson-Witting model and Marle model.In this paper, we prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial data is sufficiently close to a global equilibrium.

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