• Corpus ID: 238856800

Energy method for the Boltzmann equation of monatomic gaseous mixtures

  title={Energy method for the Boltzmann equation of monatomic gaseous mixtures},
  author={Laurent Boudin and B{\'e}r{\'e}nice Grec and Milana Pavi'c-vColi'c and Srboljub Simi'c},
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Bolzmann equation around a global equilibrium is decomposed into the sum of a macroscopic and a microscopic part, for which we obtain a priori estimates at both lower and higher orders. These estimates are obtained under a suitable smallness assumption. The assumption can be justified a… 
BGK model for multi-component gases near a global Maxwellian
Abstract. In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in [47] when the initial data is a small perturbation


Diffusion asymptotics of a kinetic model for gaseous mixtures
In this work, we investigate the asymptotic behaviour of the solutions to the non-reactive fully elastic Boltzmann equations for mixtures in the diffusive scaling. We deal with cross sections such as
Energy method for Boltzmann equation
Abstract A basic, simple energy method for the Boltzmann equation is presented here. It is based on a new macro–micro decomposition of the Boltzmann equation as well as the H-theorem. This allows us
On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases
In this paper, we propose a formal derivation of the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic gases. We use a direct extension of the model devised in [ 8 , 16 ] for
Optimal time decay of the Boltzmann system for gas mixtures
Abstract In this paper, we are concerned with the Boltzmann equation for the mixture of vapors of two gases in the whole space. Given the initial data of one gas near vacuum and the other near a
A new energy method for the Boltzmann equation
An energy method for the Boltzmann equation was proposed by Liu, Yang, and Yu [Physica D 188, 178–192 (2004)] based on the decomposition of the Boltzmann equation and its solution around the local
The Maxwell-Stefan diffusion limit for a kinetic model of mixtures with general cross sections
In this article, we derive the Maxwell-Stefan formalism from the Boltzmann equation for mixtures for general cross-sections. The derivation uses the Hilbert asymptotic method for systems at low
Boltzmann Equation: Micro-Macro Decompositions and Positivity of Shock Profiles
We introduce an elementary energy method for the Boltzmann equation based on a decomposition of the equation into macroscopic and microscopic components. The decomposition is useful for the study of
Nonlinear Stability of Rarefaction Waves for the Boltzmann Equation
It is well known that the Boltzmann equation is related to the Euler and Navier-Stokes equations in the field of gas dynamics. The relation is either for small Knudsen number, or, for dissipative
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision
A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions
Abstract We propose a kinetic model which describes a mixture of reactive gases, in which a unique continuous internal energy parameter is present. This model enables to recover at the level of its