arXiv subjects

Zhendong Fang

Publications and source records attributed to Zhendong Fang.

5 recordsLinked to original sources

arXiv2026

The small Deborah number limit for the compressible fluid-particle flows

In this paper, we consider the hydrodynamic limit for the fluid-particle flows governed by the Vlasov-Fokker-Planck equation coupled with the compressible Navier-Stokes equation as the Deborah number tends to zero. The proof is based on a formal derivation via the Hilbert expansion around the limiting system, the rigorous justification of which is completed by the refined energy estimates involving the macro-micro decomposition. Compared with the existing results obtained by the relative entropy argument ([A. Mellet and A. F. Vasseur, Comm. Math. Phys., 281 (2008), pp. 573-596]), the present work extends to a pointwise convergence of the hydrodynamic limits with an explicit rate for the fluid-particle coupled model.

math.AP↗

arXiv2025

Hydrodynamic limit of the Vlasov-Poisson-Fokker-Planck system in low-field regime

In this paper, we study the hydrodynamic limit of the scaled Vlasov-Poisson-Fokker-Planck (VPFP) system in the low-field regime. By employing the moment method, we formally derive the corresponding Drift-Diffusion-Poisson (DDP) system. Furthermore, we rigorously justify the pointwise convergence from the VPFP system to the DDP system through delicate high-order energy estimates based on the Macro-Micro decomposition. The main difficulty lies in controlling the nonlinear coupling between the kinetic and electrostatic fields and establishing uniform bounds with respect to the scaling parameter. These challenges are overcome by developing refined high-order energy methods that yield uniform energy estimates and ensure the global well-posedness of smooth solutions, without relying on any a priori assumptions for the limiting DDP system.

math.AP↗

arXiv2024

From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system

In this paper, we study the hydrodynamic limit transition from the Boltzmann equation for gas mixtures to the two-fluid macroscopic system. Employing a meticulous dimensionless analysis, we derive several novel hydrodynamic models via the moments' method. For a certain class of scaled Boltzmann equations governing gas mixtures of two species, we rigorously establish the two-fluid incompressible Navier-Stokes-Fourier system as the hydrodynamic limit. This validation is achieved through the Hilbert expansion around the global Maxwellian and refined energy estimates based on the Macro-Micro decomposition.

math.AP↗

arXiv2024

Formal derivations from Boltzmann equation to three stationary equations

In this paper, we concentrate on the connection between Boltzmann equation and stationary equations. To our knowledge, the stationary Navier-Stokes-Fourier system, the stationary Euler equations and the stationary Stokes equations are formally derived by moment estimate in the first time and extend the results of Bardos, Golse, and Levermore in J. Statist. Phys. 63(1-2), 323-344, 1991.

math.AP↗

arXiv2021

Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm's law

In this paper, we justify the convergence from the two-species Vlasov-Poisson-Boltzmann (in briefly,VPB) system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) system with Ohm's law in the context of classical solutions. We prove the uniform estimates with respect to the Knudsen number $\varepsilon$ for the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions. Consequently, we prove the convergence to the two-fluid incompressible NSFP as $\varepsilon$ go to 0.

math.AP↗