Related papers: Diffusive limit of the Boltzmann equation around R…
The rigorous justification of the hydrodynamic limits of kinetic equations in bounded domains has been actively investigated in recent years. In spite of the progress for the diffuse-reflection boundary case, the more challenging in-flow…
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…
We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we…
The fractional diffusion equation is rigorously derived as a scaling limit from a deterministic Rayleigh gas, where particles interact via short range potentials with support of size $\varepsilon$ and the background is distributed in space…
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.…
A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open…
In the paper we study the Boltzmann equation in the diffusive limit in a channel domain $\mathbb{T}^2\times (-1,1)$ for the 3D kinetic Couette flow. Our results demonstrate that the first-order approximation of the solutions is governed by…
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…
In the current work we construct a multimolecule random process which leads to the Boltzmann equation in the appropriate limit, and which is different from the deterministic real gas dynamics process. We approximate the statistical…
It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the Euler equations with viscosity and heat-conductivity…
This paper is devoted to the hydrodynamic limit for the linear Boltzmann equation, in the case of a heavy tail equilibrium and a cross section which depends on the space variable and which degenerates for large velocities, without symmetry…
Under the diffusion scaling and a scaling assumption on the microscopic component, a non-classical fluid dynamic system was derived in \cite{BGLY} that is related to the system of ghost effect derived in \cite{Sone-2} in different settings.…
We consider a kinetic model whose evolution is described by a Boltzmann-like equation for the one-particle phase space distribution $f(x,v,t)$. There are hard-sphere collisions between the particles as well as collisions with randomly fixed…
We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…
In this dissertation two-dimensional buoyancy-driven flows are investigated. While usually the Navier-Stokes equations are equipped with no-slip boundary conditions here we focus on the Navier-slip conditions that, depending on the system…
Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number $\epsilon\rightarrow 0^+$. Using the Hilbert expansion, we rigorously…
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],…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
In the present paper, we concern the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition in a two-dimensional disk to the compressible Euler equations. Due to the non-zero curvature and non-zero tangential…
In this paper, we study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures $\theta_0$ and $\theta_1$. This problem was studied by Esposito et al [13,14] where…