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Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics which has been applied to numerous problems of physical chemistry and biophysics. Its essential limitations are the neglect of correlation effects and of…
We establish the incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation with a general cut-off collision kernel in a bounded domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized…
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…
We are concerned with a mixture of Boltzmann and McKean-Vlasov type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself,and driven by a Poisson point measure with the…
The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a…
This paper investigates the Knudsen layer equation in half-space, arising from the hydrodynamic limit of the Boltzmann equation to fluid dynamics. We consider the Maxwell reflection boundary condition with accommodation coefficient…
The existence of global renormalized solutions to the Boltzmann equation with long-range interactions without angular cutoff was first established by Alexandre and Villani [Comm. Pure Appl. Math., 55(1), 30-70, 2002]. Their result relies on…
The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the…
In this paper we study weak-strong uniqueness and singular relaxation limits for the Euler--Korteweg and Navier--Stokes--Korteweg systems with non monotone pressure. Both weak-strong uniqueness and the relaxation limit are investigated…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
Many transport processes exhibit direction-dependent diffusion, described macroscopically by the full-tensor anisotropic advection--diffusion equation (ADE). Numerical discretization is demanding when the principal axes are rotated relative…
We first give hypotheses of the bicharacteristic equations corresponding to the Enskog equation with an external force. Since the collision operator of the Enskog equation is more complicated than that of the Boltzmann equation, these…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a…
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the…
By examination of the exerted electromagnetic (EM) force on boundary of an object in a few examples, we look into the compatibility of the stress tensors corresponding to different formulae of the EM force density with special relativity.…
This study investigates the steady Boltzmann equation in one spatial variable for a polyatomic single-component gas in a half-space. Inflow boundary conditions are assumed at the half-space boundary, where particles entering the half-space…
During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle…
We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…
We investigate the large-time behavior of solutions toward the combination of the boundary layer and 3-rarefaction waves to the outflow problem for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations…