相关论文: The Cauchy problem for Boltzmann bi-linear systems…
We solve the Cauchy problem for the full non-linear homogeneous Boltzmann system of equations describing multi-component monatomic gas mixtures for binary interactions in three dimensions. More precisely, we show existence and uniqueness of…
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…
This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…
This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…
This paper studies a Boltzmann-Nordheim equation in a slab with two-dimensional velocity space and pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem with large initial data in an $ L^1 \cap L^{\infty} $ setting.…
Inspired by DiPerna-Lions' work \cite{Diperna-Lions}, we study the renormalized solutions to the large-data Cauchy problem of the Boltzmann systems modeling mixture gases of monatomic and polyatomic species, in which the distribution…
A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are…
We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the…
We study the Cauchy theory for a multi-species mixture, where the different species can have different masses, in a perturbative setting on the $3$-dimensional torus. The ultimate aim of this work is to obtain existence, uniqueness and…
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and…
For the natural initial conditions $L^1$ in the density field (more generally a positive bounded Radon measure) and $L^\infty$ in the velocity field we obtain global approximate solutions to the Cauchy problem for the 3-D systems of…
A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and…
This paper studies a space-inhomogeneous Boltzmann-Nordheim equation with pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem in a setting with large bounded L1 initial data. The main results are existence,…
In this paper we study the Boltzmann equation near global Maxwellians in the $d$-dimensional whole space. A unique global-in-time mild solution to the Cauchy problem of the equation is established in a Chemin-Lerner type space with respect…
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…
The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy…
The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while…
We consider the existence of steady rarefied flows of polyatomic gas between two parallel condensed phases, where evaporation and condensation processes occur. To this end, we study the existence problem of stationary solutions in a…