Global existence and stability of mild solutions to the Boltzmann system for gas mixtures

DOI10.1090/S0033-569X-07-01068-6zbMath1160.35507OpenAlexW1998811894MaRDI QIDQ5302835

Se Eun Noh, Seok-Bae Yun, Seung-Yeal Ha

Publication date: 13 January 2009

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/distribution/qam/2007-65-04/S0033-569X-07-01068-6/home.html

zbMATH Keywords

mild solutionsgas mixturesBoltzmann systemKaniel-Shinbrot's scheme

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) PDEs in connection with quantum mechanics (35Q40)

Related Items

A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases ⋮ Existence, uniqueness and positivity of solutions for BGK models for mixtures ⋮ BGK Model for Two-Component Gases Near a Global Maxwellian ⋮ Global well-posedness of a binary-ternary Boltzmann equation ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ Boltzmann systems for gas mixtures in 1D torus ⋮ BGK model of the multi-species Uehling-Uhlenbeck equation ⋮ \(L^p\)-estimates of the Boltzmann equation around a traveling local Maxwellian

Cites Work

• Unnamed Item
• Unnamed Item
• Molecular gas dynamics. Theory, techniques, and applications.
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• The Boltzmann equation: global existence for a rare gas in an infinite vacuum
• On the nonlinear Boltzmann equation in unbounded domains
• The Boltzmann equation. I. Uniqueness and local existence
• Knudsen layer for gas mixtures
• A consistent BGK-type model for gas mixtures
• Kinetic theory and fluid dynamics
• Classical solution of the nonlinear Boltzmann equation in all \({\mathbb{R}}^ 3\): asymptotic behavior of solutions.
• Nonlinear functionals of the Boltzmann equation and uniform stability estimates
• Stability estimates of the Boltzmann equation with quantum effects
• Uniform \(L^{1}\)-stability estimate of the Boltzmann equation near a local Maxwellian
• Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall
• Kinetic theory analysis of the two-surface problem of a vapor–vapor mixture in the continuum limit
• Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation
• A kinetic model for a multicomponent gas
• On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability
• Kinetic Modeling of Gas Mixtures