arXiv subjects

Junhwa Jung

Publications and source records attributed to Junhwa Jung.

4 recordsLinked to original sources

arXiv2026

Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition

While weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was established for the Maxwell boundary condition within renormalized solutions framework [Saint.Raymond2009][Jiang-Masmoudi2017], the corresponding strong diffusive limit has remained outstanding except when the accommodation coefficient $α\sim \varepsilon^{1/2}$ [Jiang-Masmoudi2017]. We establish global in time strong diffusive limit for all accommodation coefficients $α\in [0, 1]$ within strong solutions framework. The main novelties of our proof include: (1) a $\varepsilon$-stretching method for reduction to a single-bounce $L^\infty$ estimate; (2) a dissipation estimate for a carefully constructed rotating Maxwellian in the near-specular regime $α\ll \varepsilon$.

math.AP↗

arXiv2026

Regular Lenard-Balescu equations in a Periodic Box

The Lenard-Balescu equation is a collisional kinetic model widely used in plasma physics as a Bogoliubov correction to the meanfield Vlasov theory. Unlike the classical Landau and Boltzmann collision operators, the Lenard-Balescu collisional kernel not only accounts for the binary interaction between particles, but also includes the collective meanfield effects. In this paper, we construct global smooth solutions to the regular Lenard-Balescu equation near global Maxwellians in a periodic box, thus extending the previous work by Duerinckx-Winter that treats the spatially homogenous case to the inhomogenous setting.

math.AP↗

arXiv2025

Global Diffusive Expansion of Boltzmann Equation in exterior Domain

The study of flows over an obstacle is one of the fundamental problems in fluids. In this paper we establish the global validity of the diffusive limit for the Boltzmann equations to the Navier-Stokes-Fourier system in an exterior domain. To overcome the well-known difficulty of the lack of Poincare's inequality in unbounded domain, we develop a new $L^2-L^3-L^6$ splitting to extend $L^2-L^\infty$ framework into the unbounded domain.

math.AP↗

arXiv2024

Diffusive Expansion of the Boltzmann equation for the flow past an obstacle

The exterior domain problem is essential in fluid and kinetic equations. In this paper, we establish the validity of the diffusive expansion for the Boltzmann equations to the Navier-Stokes-Fourier system up to the critical time in an exterior domain with non-zero passing flow. We apply the $L^3-L^6$ framework to the unbounded domain in this paper.

math.AP↗