相关论文: Ellipsoidal BGK model near a global Maxwellian

This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of…

In this paper, we study the initial value problem of a Boltzmann type equation with a nonlinear degenerate damping. We prove the existence of global weak solutions with large initial data, in three dimensional space. We rely on a variant…

We are concerned with the global existence of classical solutions to the barotropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. We demonstrate that the classical solutions…

We prove the unique existence and exponential decay of global in time classical solutions to the special relativistic Boltzmann equation without any angular cut-off assumptions with initial perturbations in some weighted Sobolev spaces. We…

We consider the non-isentropic compressible Navier-Stokes equations in two or three space dimensions for which the heat conduction of Fourier's law is replaced by Cattaneo's law and the classical Newtonian flow is replaced by a revised…

We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model…

Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of them is the Galilean…

The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy provides a time-reversal-symmetric framework for describing the nonequilibrium evolution of many-body systems. Despite the success of Boltzmann-based numerical approaches,…

In this paper, we are concerned with the boundary value problem in a slab for the stationary relativistic BGK model of Marle type, which is a relaxation model of the relativistic Boltzmann equation. In the case of fixed inflow boundary…

We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom…

A general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented. We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case, however, without…

We consider the semiclassical Schr\"odinger-Poisson system with a special initial data of WKB type such that the solution of the limiting hydrodynamical equation becomes time-global in dimensions at least three. We give an example of such…

A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the…

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…

In this work, we prove the convergence of strong solutions of the Boltzman equation, for initial data having polynomial decay in the velocity variable, towards those of the incompressible Navier-Stokes-Fourier system. We show in particular…

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…

In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via $BV_{loc}$ theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary…

This work proves the global stability of the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse-power intermolecular potentials, $r^{-(p-1)}$ with $p>2$, for initial…

We study a hydrodynamic limit of the Vlasov-Navier-Stokes system with external gravity force, following the framework introduced by Han-Kwan and Michel in [Han-Kwan - Michel, arXiv:2103.06668]. We answer a question raised in the latter…

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid…